Added Navier plate solution to simply supported plates. Moved Poisson analytical solution to separate file.
git-svn-id: http://svn.sintef.no/trondheim/IFEM/trunk@1203 e10b68d5-8a6e-419e-a041-bce267b0401d
This commit is contained in:
kmo
Knut Morten Okstad
parent
e52597abb6
commit
af2f3d991b
@ -7,7 +7,7 @@
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//!
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//! \author Knut Morten Okstad / SINTEF
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//!
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//! \brief Analytic solutions for some linear elasticity and Poisson problems.
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//! \brief Analytic solutions for linear elasticity problems.
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//!
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//==============================================================================
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@ -183,35 +183,87 @@ SymmTensor CurvedBeam::evaluate (const Vec3& X) const
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/*!
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\class NavierPlate
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Navier plate solution for a constant pressure load.
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Navier plate solution for a constant pressure load or
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a point load at an arbitrary position.
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Reference: S. E. Weberg, "Todimensjonal elastisitetsteori", 1975, page 62.
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Reference: S. E. Weberg, "Todimensjonal elastisitetsteori", 1975, pages 61-67.
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*/
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NavierPlate::NavierPlate (double a, double b, double t, double F,
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double E, double Poiss) : pz(F), nu(Poiss)
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NavierPlate::NavierPlate (double a, double b, double t, double E, double Poiss,
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double P) : pz(P), nu(Poiss), type(0), inc(2)
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{
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alpha = M_PI/a;
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beta = M_PI/b;
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// Calculate and print the maximum displacement (at x=a/2, y=b/2)
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// Calculate and print the maximum displacement (at the centre x=a/2, y=b/2)
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double x = 0.5*a;
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double y = 0.5*b;
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double D = E*t*t*t/(12.0-12.0*nu*nu);
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double w = 0.0;
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for (int m = 1; m < 100; m += 2)
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for (int n = 1; n < 100; n += 2)
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for (int m = 1; m < 100; m += inc)
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for (int n = 1; n < 100; n += inc)
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{
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double am = alpha*m;
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double bn = beta*n;
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double am2 = am*am;
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double bn2 = bn*bn;
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double pzmn = 16.0*pz / (M_PI*M_PI*m*n*(am2+bn2)*(am2+bn2));
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w += (pzmn/D) * sin(0.5*am*a)*sin(0.5*bn*b);
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double abmn = am*am + bn*bn;
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w += sin(am*x)*sin(bn*y) / (double(m)*double(n)*abmn*abmn);
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}
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std::cout <<"NavierPlate: wmax = "<< w << std::endl;
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w *= 16.0*pz / (D*M_PI*M_PI);
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std::streamsize oldPrec = std::cout.precision(10);
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std::cout <<"\nNavierPlate: w_max = "<< w << std::endl;
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std::cout.precision(oldPrec);
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}
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NavierPlate::NavierPlate (double a, double b, double t, double E, double Poiss,
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double P, double xi_, double eta_, double c, double d)
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: pz(P), nu(Poiss), type(2), inc(1)
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{
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alpha = M_PI/a;
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beta = M_PI/b;
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xi = xi_*a;
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eta = eta_*b;
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c2 = 0.5*c;
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d2 = 0.5*d;
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if (c == 0.0 || d == 0.0) type = 1;
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if (xi_ == 0.5 && eta_ == 0.5) inc = 2;
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// Calculate and print the displacement at the centre x=a/2, y=b/2
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double x = 0.5*a;
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double y = 0.5*b;
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double D = E*t*t*t/(12.0-12.0*nu*nu);
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double w = 0.0;
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for (int m = 1; m <= 100; m += inc)
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for (int n = 1; n <= 100; n += inc)
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{
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double am = alpha*m;
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double bn = beta*n;
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double abmn = am*am + bn*bn;
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double pzmn = sin(am*xi)*sin(bn*eta) / (abmn*abmn);
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if (type == 2)
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pzmn *= sin(am*c2)*sin(bn*d2) / (double(m)*double(n));
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w += pzmn*sin(am*x)*sin(bn*y);
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}
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if (type == 1)
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w *= 4.0*pz / (D*a*b);
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else
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w *= 16.0*pz / (D*M_PI*M_PI);
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std::streamsize oldPrec = std::cout.precision(10);
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std::cout <<"\nNavierPlate: w_centre = "<< w << std::endl;
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std::cout.precision(oldPrec);
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}
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inline double SIN(double x) { return sin(fmod(x,2.0*M_PI)); }
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inline double COS(double x) { return cos(fmod(x,2.0*M_PI)); }
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void NavierPlate::addTerms (std::vector<double>& M,
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double x, double y, int m, int n) const
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{
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@ -219,181 +271,62 @@ void NavierPlate::addTerms (std::vector<double>& M,
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double bn = beta*n;
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double am2 = am*am;
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double bn2 = bn*bn;
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double pzmn = 16.0*pz / (M_PI*M_PI*m*n*(am2+bn2)*(am2+bn2));
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M[0] += pzmn*(am2 + nu*bn2)*sin(am*x)*sin(bn*y);
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M[1] += pzmn*(bn2 + nu*am2)*sin(am*x)*sin(bn*y);
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M[2] += pzmn*(nu - 1.0)*am*bn*cos(am*x)*cos(bn*y);
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double dmn = double(m) * double(n);
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double pzmn = 0.0;
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switch (type) {
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case 0: // uniform pressure
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pzmn = 1.0 / dmn;
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break;
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case 1: // concentrated point load
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pzmn = SIN(am*xi)*SIN(bn*eta);
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break;
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case 2: // partial load
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pzmn = SIN(am*xi)*SIN(bn*eta) * SIN(am*c2)*SIN(bn*d2) / dmn;
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break;
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}
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pzmn /= (am2+bn2)*(am2+bn2);
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M[0] += pzmn*(am2 + nu*bn2)*SIN(am*x)*SIN(bn*y);
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M[1] += pzmn*(bn2 + nu*am2)*SIN(am*x)*SIN(bn*y);
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M[2] += pzmn*(nu - 1.0)*am*bn*COS(am*x)*COS(bn*y);
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}
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SymmTensor NavierPlate::evaluate (const Vec3& X) const
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{
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const int max_mn = 100;
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const double eps = 1.0e-16;
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const double eps = 1.0e-8;
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SymmTensor M(2);
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double prev = 0.0;
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for (int i = 1; i <= max_mn; i += 2)
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for (int i = 1; i <= max_mn; i += inc)
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{
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for (int m = 1; m < i; m += 2)
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this->addTerms(M,X.x,X.y,m,i);
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for (int n = 1; n < i; n += 2)
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this->addTerms(M,X.x,X.y,i,n);
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for (int j = 1; j < i; j += inc)
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{
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this->addTerms(M,X.x,X.y,i,j);
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this->addTerms(M,X.x,X.y,j,i);
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}
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this->addTerms(M,X.x,X.y,i,i);
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double norm = M.L2norm();
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if (fabs(norm-prev) < eps) break;
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#ifdef SP_DEBUG
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if (i == 1) std::cout <<"\nNavierPlate, X = "<< X.x <<" "<< X.y << std::endl;
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std::cout << i <<": "<< M(1,1) <<" "<< M(2,2) <<" "<< M(1,2)
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<<" -> "<< norm <<" "<< fabs(norm-prev)/norm << std::endl;
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#endif
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if (i%2)
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if (fabs(norm-prev) < eps*norm)
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break;
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else
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prev = norm;
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}
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if (type == 1) // concentrated load
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M *= 4.0*pz * (alpha/M_PI)*(beta/M_PI);
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else // uniform or partial pressure load
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M *= 16.0*pz / (M_PI*M_PI);
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return M;
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}
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Vec3 Square2D::evaluate (const Vec3& X) const
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{
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double x = X.x;
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double y = X.y;
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double pi = M_PI;
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Vec3 temp;
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temp.x = -pi*sin(pi*x)*(2.0-y);
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temp.y = -cos(pi*x);
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return temp;
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}
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double Square2DHeat::evaluate (const Vec3& X) const
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{
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double x = X.x;
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double y = X.y;
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double pi = M_PI;
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return -pi*pi*cos(pi*x)*(2.0-y);
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}
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Vec3 LshapePoisson::evaluate (const Vec3& X) const
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{
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double x = X.x;
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double y = X.y;
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double R = hypot(x,y);
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double pi = M_PI;
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double Rp = pow(R,-1.0/3.0);
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double th = x > 0.0 ? asin(y/R) : pi-asin(y/R);
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double frac = 2.0/3.0;
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Vec3 temp;
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temp.x = frac*Rp*sin(th/3.0);
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temp.y = -frac*Rp*cos(th/3.0);
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return temp;
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}
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Vec3 SquareSinus::evaluate (const Vec3& X) const
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{
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double x = X.x;
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double y = X.y;
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double pi = M_PI;
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Vec3 temp;
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temp.x = 2*pi*cos(2*pi*x)*sin(2*pi*y);
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temp.y = 2*pi*sin(2*pi*x)*cos(2*pi*y);
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return temp;
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}
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double SquareSinusSource::evaluate (const Vec3& X) const
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{
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double x = X.x;
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double y = X.y;
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double pi = M_PI;
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return -2*2*2*pi*pi*sin(2*pi*x)*sin(2*pi*y);
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}
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Vec3 PoissonInteriorLayer::evaluate (const Vec3& X) const
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{
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double x = X.x;
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double y = X.y;
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double pi = M_PI;
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Vec3 results;
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double root = sqrt((x-1.25)*(x-1.25)+(y+.25)*(y+.25));
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double u = SLOPE*(root-pi/3);
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results.x = -SLOPE*(x-1.25) / root / (1+u*u);
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results.y = -SLOPE*(y+0.25) / root / (1+u*u);
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return results;
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}
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double PoissonInteriorLayerSol::evaluate (const Vec3& X) const
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{
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// picked up from http://hpfem.org/hermes2d/doc/src/benchmarks.html
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double x = X.x;
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double y = X.y;
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double pi = M_PI;
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return atan(SLOPE*(sqrt((x-1.25)*(x-1.25)+(y+.25)*(y+.25))-pi/3));
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}
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double PoissonInteriorLayerSource::evaluate(const Vec3& X) const
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{
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// nabla of the u above.
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double x = X.x;
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double y = X.y;
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/****** maple did this for me ************/
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double ans = SLOPE * pow(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1), -0.3e1 / 0.2e1) * pow(0.2e1 * x - 0.250e1, 0.2e1) / (0.1e1 + SLOPE * SLOPE * pow(sqrt(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) - 0.3141592654e1 / 0.3e1, 0.2e1)) / 0.4e1 - 0.2e1 * SLOPE * pow(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1), -0.1e1 / 0.2e1) / (0.1e1 + SLOPE * SLOPE * pow(sqrt(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) - 0.3141592654e1 / 0.3e1, 0.2e1)) + pow(SLOPE, 0.3e1) / (pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) * pow(0.2e1 * x - 0.250e1, 0.2e1) * pow(0.1e1 + SLOPE * SLOPE * pow(sqrt(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) - 0.3141592654e1 / 0.3e1, 0.2e1), -0.2e1) * (sqrt(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) - 0.3141592654e1 / 0.3e1) / 0.2e1 + SLOPE * pow(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1), -0.3e1 / 0.2e1) * pow(0.2e1 * y + 0.50e0, 0.2e1) / (0.1e1 + SLOPE * SLOPE * pow(sqrt(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) - 0.3141592654e1 / 0.3e1, 0.2e1)) / 0.4e1 + pow(SLOPE, 0.3e1) / (pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) * pow(0.2e1 * y + 0.50e0, 0.2e1) * pow(0.1e1 + SLOPE * SLOPE * pow(sqrt(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) - 0.3141592654e1 / 0.3e1, 0.2e1), -0.2e1) * (sqrt(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) - 0.3141592654e1 / 0.3e1) / 0.2e1;
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/***********************************************************************/
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return ans;
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}
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Vec3 PoissonCube::evaluate (const Vec3& X) const
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{
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double x = X.x;
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double y = X.y;
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double z = X.z;
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double pi = M_PI;
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Vec3 temp;
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temp.x = -pi*cos(x*pi)*sin(y*pi)*sin(z*pi);
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temp.y = -pi*sin(x*pi)*cos(y*pi)*sin(z*pi);
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temp.z = -pi*sin(x*pi)*sin(y*pi)*cos(z*pi);
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return temp;
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}
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double PoissonCubeSource::evaluate (const Vec3& X) const
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{
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double x = X.x;
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double y = X.y;
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double z = X.z;
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double pi = M_PI;
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return 3.0*pi*pi*sin(x*pi)*sin(y*pi)*sin(z*pi);
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}
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Vec3 PoissonLine::evaluate (const Vec3& X) const
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{
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double x = X.x;
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double pi = M_PI;
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Vec3 temp;
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temp.x = -(pi/L)*cos(x*pi/L);
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return temp;
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}
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double PoissonLineSource::evaluate (const Vec3& X) const
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{
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double x = X.x;
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double pi = M_PI;
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return (pi*pi)/(L*L)*sin(pi*x/L);
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}
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@ -7,7 +7,7 @@
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//!
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//! \author Knut Morten Okstad / SINTEF
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//!
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//! \brief Analytic solutions for some linear elasticity and Poisson problems.
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//! \brief Analytic solutions for linear elasticity problems.
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//!
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//==============================================================================
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@ -152,9 +152,11 @@ private:
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class NavierPlate : public STensorFunc
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{
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public:
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//! \brief Constructor with some default parameters.
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NavierPlate(double a = 1.0, double b = 1.0, double t = 0.1, double F = 1.0,
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double E = 2.1e11, double Poiss = 0.3);
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//! \brief Constructor for plate with constant pressure load.
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NavierPlate(double a, double b, double t, double E, double Poiss, double P);
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//! \brief Constructor for plate with partial pressure or point load.
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NavierPlate(double a, double b, double t, double E, double Poiss, double P,
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double xi_, double eta_, double c = 0.0, double d = 0.0);
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//! \brief Empty destructor.
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virtual ~NavierPlate() {}
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@ -170,218 +172,13 @@ private:
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double beta; //!< pi/(plate width)
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double pz; //!< Load parameter
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double nu; //!< Poisson's ratio
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};
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/*!
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\brief Analytic solution for the Poisson equation on a square.
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*/
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class Square2D : public VecFunc
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{
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public:
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//! \brief Empty constructor.
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Square2D(double = 1.0) {}
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//! \brief Empty destructor.
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virtual ~Square2D() {}
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protected:
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//! \brief Evaluates the analytic flux vector at the point \a X.
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virtual Vec3 evaluate(const Vec3& X) const;
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};
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/*!
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\brief Heat source for the Poisson equation on a square.
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*/
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class Square2DHeat : public RealFunc
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{
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public:
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//! \brief Empty constructor.
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Square2DHeat(double = 1.0) {}
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//! \brief Empty destructor.
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virtual ~Square2DHeat() {}
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protected:
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//! \brief Evaluates the heat field at the point \a X.
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virtual double evaluate(const Vec3& X) const;
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};
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/*!
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\brief Analytic solution for the L-shape problem for the Poisson equation.
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*/
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class LshapePoisson : public VecFunc
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{
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public:
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//! \brief Empty constructor.
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LshapePoisson() {}
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//! \brief Empty destructor.
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virtual ~LshapePoisson() {}
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protected:
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//! \brief Evaluates the analytic flux vector at the point \a X.
|
||||
virtual Vec3 evaluate(const Vec3& X) const;
|
||||
};
|
||||
|
||||
/*!
|
||||
\brief Sinus-solution of the Poisson equation on a square.
|
||||
*/
|
||||
|
||||
class SquareSinus : public VecFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty constructor.
|
||||
SquareSinus() {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~SquareSinus() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the analytic flux vector at the point \a X.
|
||||
virtual Vec3 evaluate(const Vec3& X) const;
|
||||
};
|
||||
|
||||
/*!
|
||||
\brief Sinus-solution of the Poisson equation on a square.
|
||||
*/
|
||||
|
||||
class SquareSinusSource : public RealFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty constructor.
|
||||
SquareSinusSource() {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~SquareSinusSource() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the analytic flux vector at the point \a X.
|
||||
virtual double evaluate(const Vec3& X) const;
|
||||
};
|
||||
|
||||
/*!
|
||||
\brief Poisson problem with smooth solution that exhibits a steep interior layer
|
||||
*/
|
||||
class PoissonInteriorLayer : public VecFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty constructor.
|
||||
PoissonInteriorLayer(double s = 60.0) : SLOPE(s) {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~PoissonInteriorLayer() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the heat field at the point \a X.
|
||||
virtual Vec3 evaluate(const Vec3& X) const;
|
||||
|
||||
private:
|
||||
double SLOPE; //!< layer SLOPE (larger SLOPE gives problems for adaptive solvers)
|
||||
};
|
||||
|
||||
class PoissonInteriorLayerSol : public RealFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty constructor.
|
||||
PoissonInteriorLayerSol(double s = 60.0) : SLOPE(s) {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~PoissonInteriorLayerSol() {}
|
||||
protected:
|
||||
//! \brief Evaluates the exact solution of the heat distribution at the point \a X.
|
||||
virtual double evaluate(const Vec3& X) const;
|
||||
private:
|
||||
double SLOPE; //!< layer SLOPE (larger SLOPE gives problems for adaptive solvers)
|
||||
};
|
||||
|
||||
class PoissonInteriorLayerSource : public RealFunc
|
||||
{
|
||||
public:
|
||||
//! \brief default constructor.
|
||||
PoissonInteriorLayerSource(double s = 60.0) : SLOPE(s) {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~PoissonInteriorLayerSource() {}
|
||||
protected:
|
||||
virtual double evaluate(const Vec3& X) const;
|
||||
private:
|
||||
double SLOPE; //!< layer SLOPE (larger SLOPE gives problems for adaptive solvers)
|
||||
};
|
||||
|
||||
|
||||
/*!
|
||||
\brief Analytic solution for the Poisson equation on a cube.
|
||||
*/
|
||||
|
||||
class PoissonCube : public VecFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty Constructor.
|
||||
PoissonCube() {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~PoissonCube() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the analytic flux vector at the point \a X.
|
||||
virtual Vec3 evaluate(const Vec3& X) const;
|
||||
};
|
||||
|
||||
|
||||
/*!
|
||||
\brief Heat source for the Poisson equation on a cube.
|
||||
*/
|
||||
|
||||
class PoissonCubeSource : public RealFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty constructor.
|
||||
PoissonCubeSource() {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~PoissonCubeSource() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the heat field at the point \a X.
|
||||
virtual double evaluate(const Vec3& X) const;
|
||||
};
|
||||
|
||||
|
||||
/*!
|
||||
\brief Analytic solution for the Poisson equation on a line.
|
||||
*/
|
||||
|
||||
class PoissonLine : public VecFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty constructor.
|
||||
PoissonLine(double r = 1.0) : L(r) {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~PoissonLine() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the analytic flux vector at the point \a X.
|
||||
virtual Vec3 evaluate(const Vec3& X) const;
|
||||
|
||||
private:
|
||||
double L; //!< Length parameter
|
||||
};
|
||||
|
||||
|
||||
/*!
|
||||
\brief Heat source for the Poisson equation on a line.
|
||||
*/
|
||||
|
||||
class PoissonLineSource : public RealFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty constructor.
|
||||
PoissonLineSource(double r = 1.0) : L(r) {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~PoissonLineSource() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the heat field at the point \a X.
|
||||
virtual double evaluate(const Vec3& X) const;
|
||||
|
||||
private:
|
||||
double L; //!< Length parameter
|
||||
char type; //!< Load type parameter
|
||||
double xi; //!< X-position of point/partial load
|
||||
double eta; //!< Y-position of point/partial load
|
||||
double c2; //!< Partial load extension in X-direction
|
||||
double d2; //!< Partial load extension in Y-direction
|
||||
int inc; //!< Increment in Fourier term summation (1 or 2)
|
||||
};
|
||||
|
||||
#endif
|
||||
|
||||
164
src/Integrands/PoissonSolutions.C
Normal file
164
src/Integrands/PoissonSolutions.C
Normal file
@ -0,0 +1,164 @@
|
||||
// $Id$
|
||||
//==============================================================================
|
||||
//!
|
||||
//! \file PoissonSolutions.C
|
||||
//!
|
||||
//! \date Jul 1 2009
|
||||
//!
|
||||
//! \author Knut Morten Okstad / SINTEF
|
||||
//!
|
||||
//! \brief Analytic solutions for Poisson problems.
|
||||
//!
|
||||
//==============================================================================
|
||||
|
||||
#include "PoissonSolutions.h"
|
||||
#include "Vec3.h"
|
||||
|
||||
|
||||
Vec3 Square2D::evaluate (const Vec3& X) const
|
||||
{
|
||||
double x = X.x;
|
||||
double y = X.y;
|
||||
double pi = M_PI;
|
||||
|
||||
Vec3 temp;
|
||||
temp.x = -pi*sin(pi*x)*(2.0-y);
|
||||
temp.y = -cos(pi*x);
|
||||
|
||||
return temp;
|
||||
}
|
||||
|
||||
double Square2DHeat::evaluate (const Vec3& X) const
|
||||
{
|
||||
double x = X.x;
|
||||
double y = X.y;
|
||||
double pi = M_PI;
|
||||
|
||||
return -pi*pi*cos(pi*x)*(2.0-y);
|
||||
}
|
||||
|
||||
|
||||
Vec3 LshapePoisson::evaluate (const Vec3& X) const
|
||||
{
|
||||
double x = X.x;
|
||||
double y = X.y;
|
||||
double R = hypot(x,y);
|
||||
double pi = M_PI;
|
||||
double Rp = pow(R,-1.0/3.0);
|
||||
double th = x > 0.0 ? asin(y/R) : pi-asin(y/R);
|
||||
double frac = 2.0/3.0;
|
||||
|
||||
Vec3 temp;
|
||||
temp.x = frac*Rp*sin(th/3.0);
|
||||
temp.y = -frac*Rp*cos(th/3.0);
|
||||
|
||||
return temp;
|
||||
}
|
||||
|
||||
|
||||
Vec3 SquareSinus::evaluate (const Vec3& X) const
|
||||
{
|
||||
double x = X.x;
|
||||
double y = X.y;
|
||||
double pi = M_PI;
|
||||
|
||||
Vec3 temp;
|
||||
temp.x = 2*pi*cos(2*pi*x)*sin(2*pi*y);
|
||||
temp.y = 2*pi*sin(2*pi*x)*cos(2*pi*y);
|
||||
|
||||
return temp;
|
||||
}
|
||||
|
||||
double SquareSinusSource::evaluate (const Vec3& X) const
|
||||
{
|
||||
double x = X.x;
|
||||
double y = X.y;
|
||||
double pi = M_PI;
|
||||
|
||||
return -2*2*2*pi*pi*sin(2*pi*x)*sin(2*pi*y);
|
||||
}
|
||||
|
||||
|
||||
Vec3 PoissonInteriorLayer::evaluate (const Vec3& X) const
|
||||
{
|
||||
double x = X.x - 1.25;
|
||||
double y = X.y + 0.25;
|
||||
double pi = M_PI;
|
||||
Vec3 result;
|
||||
|
||||
double root = hypot(x,y);
|
||||
double u = SLOPE*(root-pi/3.0);
|
||||
result.x = -SLOPE*x / root / (1.0+u*u);
|
||||
result.y = -SLOPE*y / root / (1.0+u*u);
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
/*!
|
||||
\class PoissonInteriorLayerSol
|
||||
|
||||
Picked up from http://hpfem.org/hermes2d/doc/src/benchmarks.html
|
||||
*/
|
||||
double PoissonInteriorLayerSol::evaluate (const Vec3& X) const
|
||||
{
|
||||
double x = X.x;
|
||||
double y = X.y;
|
||||
double pi = M_PI;
|
||||
return atan(SLOPE*(hypot(x-1.25,y+0.25)-pi/3.0));
|
||||
}
|
||||
|
||||
double PoissonInteriorLayerSource::evaluate (const Vec3& X) const
|
||||
{
|
||||
double x = X.x;
|
||||
double y = X.y;
|
||||
|
||||
/****** maple did this for me (nabla of the u above) ************/
|
||||
return SLOPE * pow(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1), -0.3e1 / 0.2e1) * pow(0.2e1 * x - 0.250e1, 0.2e1) / (0.1e1 + SLOPE * SLOPE * pow(sqrt(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) - 0.3141592654e1 / 0.3e1, 0.2e1)) / 0.4e1 - 0.2e1 * SLOPE * pow(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1), -0.1e1 / 0.2e1) / (0.1e1 + SLOPE * SLOPE * pow(sqrt(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) - 0.3141592654e1 / 0.3e1, 0.2e1)) + pow(SLOPE, 0.3e1) / (pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) * pow(0.2e1 * x - 0.250e1, 0.2e1) * pow(0.1e1 + SLOPE * SLOPE * pow(sqrt(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) - 0.3141592654e1 / 0.3e1, 0.2e1), -0.2e1) * (sqrt(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) - 0.3141592654e1 / 0.3e1) / 0.2e1 + SLOPE * pow(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1), -0.3e1 / 0.2e1) * pow(0.2e1 * y + 0.50e0, 0.2e1) / (0.1e1 + SLOPE * SLOPE * pow(sqrt(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) - 0.3141592654e1 / 0.3e1, 0.2e1)) / 0.4e1 + pow(SLOPE, 0.3e1) / (pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) * pow(0.2e1 * y + 0.50e0, 0.2e1) * pow(0.1e1 + SLOPE * SLOPE * pow(sqrt(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) - 0.3141592654e1 / 0.3e1, 0.2e1), -0.2e1) * (sqrt(pow(x - 0.125e1, 0.2e1) + pow(y + 0.25e0, 0.2e1)) - 0.3141592654e1 / 0.3e1) / 0.2e1;
|
||||
/****************************************************************************/
|
||||
}
|
||||
|
||||
|
||||
Vec3 PoissonCube::evaluate (const Vec3& X) const
|
||||
{
|
||||
double x = X.x;
|
||||
double y = X.y;
|
||||
double z = X.z;
|
||||
double pi = M_PI;
|
||||
|
||||
Vec3 temp;
|
||||
temp.x = -pi*cos(x*pi)*sin(y*pi)*sin(z*pi);
|
||||
temp.y = -pi*sin(x*pi)*cos(y*pi)*sin(z*pi);
|
||||
temp.z = -pi*sin(x*pi)*sin(y*pi)*cos(z*pi);
|
||||
|
||||
return temp;
|
||||
}
|
||||
|
||||
double PoissonCubeSource::evaluate (const Vec3& X) const
|
||||
{
|
||||
double x = X.x;
|
||||
double y = X.y;
|
||||
double z = X.z;
|
||||
double pi = M_PI;
|
||||
|
||||
return 3.0*pi*pi*sin(x*pi)*sin(y*pi)*sin(z*pi);
|
||||
}
|
||||
|
||||
|
||||
Vec3 PoissonLine::evaluate (const Vec3& X) const
|
||||
{
|
||||
double x = X.x;
|
||||
double pi = M_PI;
|
||||
|
||||
Vec3 temp;
|
||||
temp.x = -(pi/L)*cos(x*pi/L);
|
||||
|
||||
return temp;
|
||||
}
|
||||
|
||||
double PoissonLineSource::evaluate (const Vec3& X) const
|
||||
{
|
||||
double x = X.x;
|
||||
double pi = M_PI;
|
||||
|
||||
return (pi*pi)/(L*L)*sin(pi*x/L);
|
||||
}
|
||||
242
src/Integrands/PoissonSolutions.h
Normal file
242
src/Integrands/PoissonSolutions.h
Normal file
@ -0,0 +1,242 @@
|
||||
// $Id$
|
||||
//==============================================================================
|
||||
//!
|
||||
//! \file PoissonSolutions.h
|
||||
//!
|
||||
//! \date Jul 1 2009
|
||||
//!
|
||||
//! \author Knut Morten Okstad / SINTEF
|
||||
//!
|
||||
//! \brief Analytic solutions for Poisson problems.
|
||||
//!
|
||||
//==============================================================================
|
||||
|
||||
#ifndef _POISSON_SOLUTIONS_H
|
||||
#define _POISSON_SOLUTIONS_H
|
||||
|
||||
#include "Function.h"
|
||||
|
||||
|
||||
/*!
|
||||
\brief Analytic solution for the Poisson equation on a square domain.
|
||||
*/
|
||||
|
||||
class Square2D : public VecFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty constructor.
|
||||
Square2D(double = 1.0) {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~Square2D() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the analytic flux vector at the point \a X.
|
||||
virtual Vec3 evaluate(const Vec3& X) const;
|
||||
};
|
||||
|
||||
|
||||
/*!
|
||||
\brief Heat source for the Poisson equation on a square domain.
|
||||
*/
|
||||
|
||||
class Square2DHeat : public RealFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty constructor.
|
||||
Square2DHeat(double = 1.0) {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~Square2DHeat() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the heat field at the point \a X.
|
||||
virtual double evaluate(const Vec3& X) const;
|
||||
};
|
||||
|
||||
|
||||
/*!
|
||||
\brief Analytic solution for the Poisson equation on the L-shape domain.
|
||||
*/
|
||||
|
||||
class LshapePoisson : public VecFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty constructor.
|
||||
LshapePoisson() {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~LshapePoisson() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the analytic flux vector at the point \a X.
|
||||
virtual Vec3 evaluate(const Vec3& X) const;
|
||||
};
|
||||
|
||||
|
||||
/*!
|
||||
\brief Sinusoidal solution of the Poisson equation on a square domain.
|
||||
*/
|
||||
|
||||
class SquareSinus : public VecFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty constructor.
|
||||
SquareSinus() {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~SquareSinus() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the analytic flux vector at the point \a X.
|
||||
virtual Vec3 evaluate(const Vec3& X) const;
|
||||
};
|
||||
|
||||
|
||||
/*!
|
||||
\brief Heat source for the sinusoidal solution on a square domain.
|
||||
*/
|
||||
|
||||
class SquareSinusSource : public RealFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty constructor.
|
||||
SquareSinusSource() {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~SquareSinusSource() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the heat field at the point \a X.
|
||||
virtual double evaluate(const Vec3& X) const;
|
||||
};
|
||||
|
||||
|
||||
/*!
|
||||
\brief Poisson problem with smooth solution and a steep interior layer.
|
||||
*/
|
||||
|
||||
class PoissonInteriorLayer : public VecFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Default constructor.
|
||||
PoissonInteriorLayer(double s = 60.0) : SLOPE(s) {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~PoissonInteriorLayer() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the heat flux at the point \a X.
|
||||
virtual Vec3 evaluate(const Vec3& X) const;
|
||||
|
||||
private:
|
||||
double SLOPE; //!< layer SLOPE (large value gives problems in adaptive solver)
|
||||
};
|
||||
|
||||
|
||||
class PoissonInteriorLayerSol : public RealFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Default constructor.
|
||||
PoissonInteriorLayerSol(double s = 60.0) : SLOPE(s) {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~PoissonInteriorLayerSol() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the exact temperature distribution at the point \a X.
|
||||
virtual double evaluate(const Vec3& X) const;
|
||||
|
||||
private:
|
||||
double SLOPE; //!< layer SLOPE
|
||||
};
|
||||
|
||||
|
||||
class PoissonInteriorLayerSource : public RealFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Default constructor.
|
||||
PoissonInteriorLayerSource(double s = 60.0) : SLOPE(s) {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~PoissonInteriorLayerSource() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the heat field at the point \a X.
|
||||
virtual double evaluate(const Vec3& X) const;
|
||||
|
||||
private:
|
||||
double SLOPE; //!< layer SLOPE
|
||||
};
|
||||
|
||||
|
||||
/*!
|
||||
\brief Analytic solution for the Poisson equation on a cube domain.
|
||||
*/
|
||||
|
||||
class PoissonCube : public VecFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty Constructor.
|
||||
PoissonCube() {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~PoissonCube() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the analytic flux vector at the point \a X.
|
||||
virtual Vec3 evaluate(const Vec3& X) const;
|
||||
};
|
||||
|
||||
|
||||
/*!
|
||||
\brief Heat source for the Poisson equation on a cube domain.
|
||||
*/
|
||||
|
||||
class PoissonCubeSource : public RealFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Empty constructor.
|
||||
PoissonCubeSource() {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~PoissonCubeSource() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the heat field at the point \a X.
|
||||
virtual double evaluate(const Vec3& X) const;
|
||||
};
|
||||
|
||||
|
||||
/*!
|
||||
\brief Analytic solution for the Poisson equation on a line domain.
|
||||
*/
|
||||
|
||||
class PoissonLine : public VecFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Default constructor.
|
||||
PoissonLine(double r = 1.0) : L(r) {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~PoissonLine() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the analytic flux vector at the point \a X.
|
||||
virtual Vec3 evaluate(const Vec3& X) const;
|
||||
|
||||
private:
|
||||
double L; //!< Length parameter
|
||||
};
|
||||
|
||||
|
||||
/*!
|
||||
\brief Heat source for the Poisson equation on a line.
|
||||
*/
|
||||
|
||||
class PoissonLineSource : public RealFunc
|
||||
{
|
||||
public:
|
||||
//! \brief Default constructor.
|
||||
PoissonLineSource(double r = 1.0) : L(r) {}
|
||||
//! \brief Empty destructor.
|
||||
virtual ~PoissonLineSource() {}
|
||||
|
||||
protected:
|
||||
//! \brief Evaluates the heat field at the point \a X.
|
||||
virtual double evaluate(const Vec3& X) const;
|
||||
|
||||
private:
|
||||
double L; //!< Length parameter
|
||||
};
|
||||
|
||||
#endif
|
||||
Loading…
Reference in New Issue
Block a user