int main(int, char**)
{
cout.precision(3);
int n = 10000;
VectorXd x(n), b(n);
SparseMatrix<double> A(n,n);
/* ... fill A and b ... */
BiCGSTAB<SparseMatrix<double> > solver;
solver.compute(A);
x = solver.solve(b);
std::cout << "#iterations: " << solver.iterations() << std::endl;
std::cout << "estimated error: " << solver.error() << std::endl;
/* ... update b ... */
x = solver.solve(b); // solve again
return 0;
}
int main() {
unsigned int end_step = END_STEP;
double v = V,
h = 1.0 / (N + 1),
dt = MU * h * h / v,
c = 0.5;
// Initialize the temperature vector and fill with the square wave
VectorXd u = VectorXd::Zero(N * N);
fourier2DSquare (u);
double mu = v * dt / (h * h);
if (mu > 0.5)
cerr << "Warning! Mu = " << mu << "; Solution may contain unphysical oscillations!" << endl;
MatrixXd BBlock = MatrixXd::Zero (N, N);
BBlock.diagonal (0) = VectorXd::Constant (N, -4 * mu);
BBlock.diagonal (1) = BBlock.diagonal (-1) = VectorXd::Constant (N - 1, mu);
MatrixXd A = MatrixXd::Zero(N * N, N * N);
A.block<N, N>(0, 0) = BBlock;
for (unsigned int i = 0; i < N - 1; ++i) {
A.block<N, N>(N * (i + 1), N * (i + 1)) = BBlock;
A.block<N, N>(N * (i + 1), N * i) = A.block<N, N>(N * i, N * (i + 1)) =
MatrixXd::Identity(N, N) * mu;
}
displayField(u, 0, c);
BiCGSTAB<MatrixXd> solver;
for (unsigned int timestep = 1; timestep < end_step; ++timestep) {
c = 0.5;
VectorXd rhs = (MatrixXd::Identity(N * N, N * N) + c * A) * u;
MatrixXd B = (MatrixXd::Identity(N * N, N * N) - (1 - c) * A);
solver.compute(B);
u = solver.solve(rhs);
cerr << "residual: " << (B * u - rhs).norm() << endl;
displayField(u, timestep, c);
}
return 0;
}
