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fix(ode): iteration matrix using dt instead of c #3294

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fix(ode): iteration matrix using dt instead of c #3294

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6 changes: 4 additions & 2 deletions ode/impl/KokkosODE_BDF_impl.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -129,10 +129,12 @@ struct BDF_system_wrapper2 {
if (compute_jac) {
mySys.evaluate_jacobian(t, dt, y, jac);

// J = I - dt*(df/dy)
// Jacobian of the corrector residual psi + (y - y_predict) - c*f:
// J = I - c*(df/dy), with c = dt/alpha[order].
// This must use the same c that scales f in residual()
for (int rowIdx = 0; rowIdx < neqs; ++rowIdx) {
for (int colIdx = 0; colIdx < neqs; ++colIdx) {
jac(rowIdx, colIdx) = -dt * jac(rowIdx, colIdx);
jac(rowIdx, colIdx) = -c * jac(rowIdx, colIdx);
}
jac(rowIdx, rowIdx) += 1.0;
}
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13 changes: 12 additions & 1 deletion ode/unit_test/Test_ODE_BDF.hpp
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Expand Up @@ -711,8 +711,19 @@ void test_BDF_adaptive_stiff() {

auto y_new_h = Kokkos::create_mirror_view(y_new);
Kokkos::deep_copy(y_new_h, y_new);
std::cout << "Stiff Chemistry solution at t=500: {" << y_new_h(0) << ", " << y_new_h(1) << ", " << y_new_h(2) << "}"
std::cout << "Stiff Chemistry solution at t=350: {" << y_new_h(0) << ", " << y_new_h(1) << ", " << y_new_h(2) << "}"
<< std::endl;

// Reference solution at t=350 computed with SciPy's Radau integrator
// using rtol=1e-12 and atol=1e-14. BDFSolve integrates with rtol=1e-3
// so we check the solution with a relative tolerance of 5e-3.
// Scaling the Jacobian of the corrector residual with dt instead of
// c=dt/alpha[order] leads to relative errors around 9e-3 which this
// test would catch, see issue #5.
const scalar_type y_ref[3] = {4.6713854e-01, 3.4400401e-06, 5.3285802e-01};
EXPECT_NEAR_KK_REL(y_new_h(0), y_ref[0], 5.0e-3);
EXPECT_NEAR_KK_REL(y_new_h(1), y_ref[1], 5.0e-3);
EXPECT_NEAR_KK_REL(y_new_h(2), y_ref[2], 5.0e-3);
}

} // namespace Test
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