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MLNodeABecLaplacian (AMReX-Codes#3559)
Add a new Linear Opearator class MLNodeABecLaplacian. It solves `(alpha * a - beta * (del dot b grad)) phi = rhs`, where a, phi and rhs are nodal MultiFabs and b is cell-centered. It works in 2D and 3D, CPU and GPU. So far it works only for single level. There is an example of using it at Tests/LinearSolvers/ABecLaplacian_C as prob_type=4. The test problem converges at the second order. --------- Co-authored-by: Andy Nonaka <[email protected]>
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‎Src/LinearSolvers/CMakeLists.txt

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@@ -49,6 +49,10 @@ foreach(D IN LISTS AMReX_SPACEDIM)
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MLMG/AMReX_MLEBNodeFDLaplacian.cpp
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MLMG/AMReX_MLEBNodeFDLap_K.H
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MLMG/AMReX_MLEBNodeFDLap_${D}D_K.H
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MLMG/AMReX_MLNodeABecLaplacian.H
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MLMG/AMReX_MLNodeABecLaplacian.cpp
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MLMG/AMReX_MLNodeABecLap_K.H
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MLMG/AMReX_MLNodeABecLap_${D}D_K.H
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)
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if (D EQUAL 3)

‎Src/LinearSolvers/MLMG/AMReX_MLNodeABecLap_1D_K.H

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#ifndef AMREX_MLNODEABECLAP_1D_K_H_
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#define AMREX_MLNODEABECLAP_1D_K_H_
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namespace amrex {
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inline void
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mlndabeclap_gauss_seidel_aa (Box const& /*bx*/, Array4<Real> const& /*sol*/,
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Array4<Real const> const& /*rhs*/,
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Real /*alpha*/, Real /*beta*/,
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Array4<Real const> const& /*acf*/,
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Array4<Real const> const& /*bcf*/,
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Array4<int const> const& /*msk*/,
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GpuArray<Real,AMREX_SPACEDIM> const& /*dxinv*/) noexcept
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{}
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AMREX_GPU_DEVICE AMREX_FORCE_INLINE void
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mlndabeclap_jacobi_aa (int /*i*/, int /*j*/, int /*k*/,
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Array4<Real> const& /*sol*/,
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Real /*lap*/,
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Array4<Real const> const& /*rhs*/,
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Real /*alpha*/, Real /*beta*/,
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Array4<Real const> const& /*acf*/,
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Array4<Real const> const& /*bcf*/,
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Array4<int const> const& /*msk*/,
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GpuArray<Real,AMREX_SPACEDIM> const& /*dxinv*/) noexcept
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{}
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}
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#endif

‎Src/LinearSolvers/MLMG/AMReX_MLNodeABecLap_2D_K.H

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#ifndef AMREX_MLNODEABECLAP_2D_K_H_
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#define AMREX_MLNODEABECLAP_2D_K_H_
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namespace amrex {
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inline void
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mlndabeclap_gauss_seidel_aa (Box const& bx, Array4<Real> const& sol,
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Array4<Real const> const& rhs,
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Real alpha, Real beta,
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Array4<Real const> const& acf,
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Array4<Real const> const& bcf,
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Array4<int const> const& msk,
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GpuArray<Real,AMREX_SPACEDIM> const& dxinv) noexcept
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{
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Real facx = Real(1.0/6.0)*dxinv[0]*dxinv[0];
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Real facy = Real(1.0/6.0)*dxinv[1]*dxinv[1];
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Real fxy = facx + facy;
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Real f2xmy = Real(2.0)*facx - facy;
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Real fmx2y = Real(2.0)*facy - facx;
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amrex::Loop(bx, [=] (int i, int j, int k) noexcept
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{
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if (msk(i,j,k)) {
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sol(i,j,k) = Real(0.0);
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} else {
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Real s0 = (-Real(2.0))*fxy*(bcf(i-1,j-1,k)+bcf(i,j-1,k)+bcf(i-1,j,k)+bcf(i,j,k));
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Real lap = sol(i-1,j-1,k)*fxy*bcf(i-1,j-1,k)
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+ sol(i+1,j-1,k)*fxy*bcf(i ,j-1,k)
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+ sol(i-1,j+1,k)*fxy*bcf(i-1,j ,k)
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+ sol(i+1,j+1,k)*fxy*bcf(i ,j ,k)
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+ sol(i-1,j,k)*f2xmy*(bcf(i-1,j-1,k)+bcf(i-1,j,k))
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+ sol(i+1,j,k)*f2xmy*(bcf(i ,j-1,k)+bcf(i ,j,k))
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+ sol(i,j-1,k)*fmx2y*(bcf(i-1,j-1,k)+bcf(i,j-1,k))
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+ sol(i,j+1,k)*fmx2y*(bcf(i-1,j ,k)+bcf(i,j ,k))
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+ sol(i,j,k)*s0;
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Real Ax = alpha*acf(i,j,k)*sol(i,j,k) - beta*lap;
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sol(i,j,k) += (rhs(i,j,k) - Ax) / (alpha*acf(i,j,k)-beta*s0);
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}
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});
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}
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AMREX_GPU_DEVICE AMREX_FORCE_INLINE void
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mlndabeclap_jacobi_aa (int i, int j, int k, Array4<Real> const& sol,
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Real lap, Array4<Real const> const& rhs,
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Real alpha, Real beta,
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Array4<Real const> const& acf,
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Array4<Real const> const& bcf,
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Array4<int const> const& msk,
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GpuArray<Real,AMREX_SPACEDIM> const& dxinv) noexcept
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{
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if (msk(i,j,k)) {
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sol(i,j,k) = Real(0.0);
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} else {
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Real fac = -Real(2.0/6.0)*(dxinv[0]*dxinv[0] + dxinv[1]*dxinv[1]);
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Real s0 = fac*(bcf(i-1,j-1,k)+bcf(i,j-1,k)+bcf(i-1,j,k)+bcf(i,j,k));
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Real Ax = alpha*acf(i,j,k)*sol(i,j,k) - beta*lap;
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sol(i,j,k) += Real(2.0/3.0) * (rhs(i,j,k) - Ax)
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/ (alpha*acf(i,j,k)-beta*s0);
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}
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}
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}
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#endif

‎Src/LinearSolvers/MLMG/AMReX_MLNodeABecLap_3D_K.H

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#ifndef AMREX_MLNODEABECLAP_3D_K_H_
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#define AMREX_MLNODEABECLAP_3D_K_H_
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namespace amrex {
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inline void
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mlndabeclap_gauss_seidel_aa (Box const& bx, Array4<Real> const& sol,
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Array4<Real const> const& rhs,
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Real alpha, Real beta,
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Array4<Real const> const& acf,
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Array4<Real const> const& bcf,
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Array4<int const> const& msk,
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GpuArray<Real,AMREX_SPACEDIM> const& dxinv) noexcept
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{
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Real facx = Real(1.0/36.0)*dxinv[0]*dxinv[0];
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Real facy = Real(1.0/36.0)*dxinv[1]*dxinv[1];
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Real facz = Real(1.0/36.0)*dxinv[2]*dxinv[2];
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Real fxyz = facx + facy + facz;
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Real fmx2y2z = -facx + Real(2.0)*facy + Real(2.0)*facz;
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Real f2xmy2z = Real(2.0)*facx - facy + Real(2.0)*facz;
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Real f2x2ymz = Real(2.0)*facx + Real(2.0)*facy - facz;
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Real f4xm2ym2z = Real(4.0)*facx - Real(2.0)*facy - Real(2.0)*facz;
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Real fm2x4ym2z = -Real(2.0)*facx + Real(4.0)*facy - Real(2.0)*facz;
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Real fm2xm2y4z = -Real(2.0)*facx - Real(2.0)*facy + Real(4.0)*facz;
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amrex::LoopOnCpu(bx, [=] (int i, int j, int k) noexcept
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{
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if (msk(i,j,k)) {
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sol(i,j,k) = Real(0.0);
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} else {
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Real s0 = Real(-4.0)*fxyz*(bcf(i-1,j-1,k-1)+bcf(i,j-1,k-1)+bcf(i-1,j,k-1)+bcf(i,j,k-1)
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+bcf(i-1,j-1,k )+bcf(i,j-1,k )+bcf(i-1,j,k )+bcf(i,j,k ));
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Real lap = sol(i,j,k)*s0
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+ fxyz*(sol(i-1,j-1,k-1)*bcf(i-1,j-1,k-1)
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+ sol(i+1,j-1,k-1)*bcf(i ,j-1,k-1)
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+ sol(i-1,j+1,k-1)*bcf(i-1,j ,k-1)
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+ sol(i+1,j+1,k-1)*bcf(i ,j ,k-1)
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+ sol(i-1,j-1,k+1)*bcf(i-1,j-1,k )
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+ sol(i+1,j-1,k+1)*bcf(i ,j-1,k )
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+ sol(i-1,j+1,k+1)*bcf(i-1,j ,k )
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+ sol(i+1,j+1,k+1)*bcf(i ,j ,k ))
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+ fmx2y2z*(sol(i ,j-1,k-1)*(bcf(i-1,j-1,k-1)+bcf(i,j-1,k-1))
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+ sol(i ,j+1,k-1)*(bcf(i-1,j ,k-1)+bcf(i,j ,k-1))
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+ sol(i ,j-1,k+1)*(bcf(i-1,j-1,k )+bcf(i,j-1,k ))
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+ sol(i ,j+1,k+1)*(bcf(i-1,j ,k )+bcf(i,j ,k )))
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+ f2xmy2z*(sol(i-1,j ,k-1)*(bcf(i-1,j-1,k-1)+bcf(i-1,j,k-1))
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+ sol(i+1,j ,k-1)*(bcf(i ,j-1,k-1)+bcf(i ,j,k-1))
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+ sol(i-1,j ,k+1)*(bcf(i-1,j-1,k )+bcf(i-1,j,k ))
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+ sol(i+1,j ,k+1)*(bcf(i ,j-1,k )+bcf(i ,j,k )))
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+ f2x2ymz*(sol(i-1,j-1,k )*(bcf(i-1,j-1,k-1)+bcf(i-1,j-1,k))
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+ sol(i+1,j-1,k )*(bcf(i ,j-1,k-1)+bcf(i ,j-1,k))
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+ sol(i-1,j+1,k )*(bcf(i-1,j ,k-1)+bcf(i-1,j ,k))
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+ sol(i+1,j+1,k )*(bcf(i ,j ,k-1)+bcf(i ,j ,k)))
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+ f4xm2ym2z*(sol(i-1,j,k)*(bcf(i-1,j-1,k-1)+bcf(i-1,j,k-1)+bcf(i-1,j-1,k)+bcf(i-1,j,k))
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+ sol(i+1,j,k)*(bcf(i ,j-1,k-1)+bcf(i ,j,k-1)+bcf(i ,j-1,k)+bcf(i ,j,k)))
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+ fm2x4ym2z*(sol(i,j-1,k)*(bcf(i-1,j-1,k-1)+bcf(i,j-1,k-1)+bcf(i-1,j-1,k)+bcf(i,j-1,k))
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+ sol(i,j+1,k)*(bcf(i-1,j ,k-1)+bcf(i,j ,k-1)+bcf(i-1,j ,k)+bcf(i,j ,k)))
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+ fm2xm2y4z*(sol(i,j,k-1)*(bcf(i-1,j-1,k-1)+bcf(i,j-1,k-1)+bcf(i-1,j,k-1)+bcf(i,j,k-1))
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+ sol(i,j,k+1)*(bcf(i-1,j-1,k )+bcf(i,j-1,k )+bcf(i-1,j,k )+bcf(i,j,k )));
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Real Ax = alpha*acf(i,j,k)*sol(i,j,k) - beta*lap;
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sol(i,j,k) += (rhs(i,j,k) - Ax) / (alpha*acf(i,j,k)-beta*s0);
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}
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});
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}
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AMREX_GPU_DEVICE AMREX_FORCE_INLINE void
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mlndabeclap_jacobi_aa (int i, int j, int k, Array4<Real> const& sol,
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Real lap, Array4<Real const> const& rhs,
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Real alpha, Real beta,
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Array4<Real const> const& acf,
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Array4<Real const> const& bcf,
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Array4<int const> const& msk,
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GpuArray<Real,AMREX_SPACEDIM> const& dxinv) noexcept
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{
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if (msk(i,j,k)) {
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sol(i,j,k) = Real(0.0);
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} else {
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Real fxyz = Real(-4.0 / 36.0)*(dxinv[0]*dxinv[0] +
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dxinv[1]*dxinv[1] +
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dxinv[2]*dxinv[2]);
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Real s0 = fxyz*(bcf(i-1,j-1,k-1)+bcf(i,j-1,k-1)+bcf(i-1,j,k-1)+bcf(i,j,k-1)
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+bcf(i-1,j-1,k )+bcf(i,j-1,k )+bcf(i-1,j,k )+bcf(i,j,k));
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Real Ax = alpha*acf(i,j,k)*sol(i,j,k) - beta*lap;
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sol(i,j,k) += Real(2.0/3.0) * (rhs(i,j,k) - Ax)
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/ (alpha*acf(i,j,k)-beta*s0);
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}
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}
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}
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#endif

‎Src/LinearSolvers/MLMG/AMReX_MLNodeABecLap_K.H

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#ifndef AMREX_MLNODEABECLAP_K_H_
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#define AMREX_MLNODEABECLAP_K_H_
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#include <AMReX_Config.H>
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#if (AMREX_SPACEDIM == 1)
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#include <AMReX_MLNodeABecLap_1D_K.H>
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#elif (AMREX_SPACEDIM == 2)
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#include <AMReX_MLNodeABecLap_2D_K.H>
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#else
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#include <AMReX_MLNodeABecLap_3D_K.H>
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#endif
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#endif

‎Src/LinearSolvers/MLMG/AMReX_MLNodeABecLaplacian.H

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#ifndef AMREX_MLNODEABECLAPLACIAN_H_
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#define AMREX_MLNODEABECLAPLACIAN_H_
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#include <AMReX_Config.H>
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#include <AMReX_MLNodeLinOp.H>
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namespace amrex {
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// (alpha * a - beta * (del dot b grad)) phi = rhs
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// a, phi and rhs are nodal. b is cell-centered.
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class MLNodeABecLaplacian
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: public MLNodeLinOp
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{
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public:
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MLNodeABecLaplacian () = default;
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MLNodeABecLaplacian (const Vector<Geometry>& a_geom,
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const Vector<BoxArray>& a_grids,
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const Vector<DistributionMapping>& a_dmap,
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const LPInfo& a_info = LPInfo(),
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const Vector<FabFactory<FArrayBox> const*>& a_factory = {});
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~MLNodeABecLaplacian () override = default;
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MLNodeABecLaplacian (const MLNodeABecLaplacian&) = delete;
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MLNodeABecLaplacian (MLNodeABecLaplacian&&) = delete;
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MLNodeABecLaplacian& operator= (const MLNodeABecLaplacian&) = delete;
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MLNodeABecLaplacian& operator= (MLNodeABecLaplacian&&) = delete;
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void define (const Vector<Geometry>& a_geom,
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const Vector<BoxArray>& a_grids,
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const Vector<DistributionMapping>& a_dmap,
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const LPInfo& a_info = LPInfo(),
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const Vector<FabFactory<FArrayBox> const*>& a_factory = {});
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std::string name () const override { return std::string("MLNodeABecLaplacian"); }
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void setScalars (Real a, Real b) {
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m_a_scalar = a;
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m_b_scalar = b;
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}
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void setACoeffs (int amrlev, Real a_acoef);
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void setACoeffs (int amrlev, const MultiFab& a_acoef);
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void setBCoeffs (int amrlev, Real a_bcoef);
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void setBCoeffs (int amrlev, const MultiFab& a_bcoef);
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void Fapply (int amrlev, int mglev, MultiFab& out, const MultiFab& in) const final;
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void Fsmooth (int amrlev, int mglev, MultiFab& sol, const MultiFab& rhs) const final;
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void fixUpResidualMask (int amrlev, iMultiFab& resmsk) final;
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bool isSingular (int /*amrlev*/) const final { return false; }
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bool isBottomSingular () const final { return false; }
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void restriction (int amrlev, int cmglev, MultiFab& crse, MultiFab& fine) const final;
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void interpolation (int amrlev, int fmglev, MultiFab& fine, const MultiFab& crse) const final;
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void averageDownSolutionRHS (int camrlev, MultiFab& crse_sol, MultiFab& crse_rhs,
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const MultiFab& fine_sol, const MultiFab& fine_rhs) final;
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void reflux (int crse_amrlev,
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MultiFab& res, const MultiFab& crse_sol, const MultiFab& crse_rhs,
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MultiFab& fine_res, MultiFab& fine_sol, const MultiFab& fine_rhs) const final;
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void prepareForSolve () final;
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void averageDownCoeffs ();
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void averageDownCoeffsToCoarseAmrLevel (int flev);
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void averageDownCoeffsSameAmrLevel (int amrlev);
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private:
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Real m_a_scalar = std::numeric_limits<Real>::quiet_NaN();
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Real m_b_scalar = std::numeric_limits<Real>::quiet_NaN();
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Vector<Vector<MultiFab> > m_a_coeffs;
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Vector<Vector<MultiFab> > m_b_coeffs;
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};
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}
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#endif

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