Helmholtz with PML

The following routines return a simple second-order discretization of the constant coefficient Helmholtz equation over \([0,1]^d\) with Perfectly Matched Layer boundary conditions with profile defined by the amplitude \(\sigma\) and exponent pmlExp, discretized over numPmlPoints grid points.

C++ API

void HelmholtzPML(Matrix<Complex<Real>> &H, Int n, Complex<Real> shift, Int numPmlPoints, Real sigma, Real pmlExp)

void HelmholtzPML(AbstractDistMatrix<Complex<Real>> &H, Int n, Complex<Real> shift, Int numPmlPoints, Real sigma, Real pmlExp)

1D Helmholtz

void HelmholtzPML(Matrix<Complex<Real>> &H, Int nx, Int ny, Complex<Real> shift, Int numPmlPoints, Real sigma, Real pmlExp)

void HelmholtzPML(AbstractDistMatrix<Complex<Real>> &H, Int nx, Int ny, Complex<Real> shift, Int numPmlPoints, Real sigma, Real pmlExp)

2D Helmholtz

void HelmholtzPML(Matrix<Complex<Real>> &H, Int nx, Int ny, Int nz, Complex<Real> shift, Int numPmlPoints, Real sigma, Real pmlExp)

void HelmholtzPML(AbstractDistMatrix<Complex<Real>> &H, Int nx, Int ny, Int nz, Complex<Real> shift, Int numPmlPoints, Real sigma, Real pmlExp)

3D Helmholtz

C API

ElError ElHelmholtzPML1D_c(ElMatrix_c H, ElInt nx, complex_float omega, ElInt numPmlPoints, float sigma, float pmlExp)

ElError ElHelmholtzPML1D_z(ElMatrix_z H, ElInt nx, complex_double omega, ElInt numPmlPoints, double sigma, double pmlExp)

ElError ElHelmholtzPML1DDist_c(ElDistMatrix_c H, ElInt nx, complex_float omega, ElInt numPmlPoints, float sigma, float pmlExp)

ElError ElHelmholtzPML1DDist_z(ElDistMatrix_z H, ElInt nx, complex_double omega, ElInt numPmlPoints, double sigma, double pmlExp)

1D Helmholtz

ElError ElHelmholtzPML2D_c(ElMatrix_c H, ElInt nx, ElInt ny, complex_float omega, ElInt numPmlPoints, float sigma, float pmlExp)

ElError ElHelmholtzPML2D_z(ElMatrix_z H, ElInt nx, ElInt ny, complex_double omega, ElInt numPmlPoints, double sigma, double pmlExp)

ElError ElHelmholtzPML2DDist_c(ElDistMatrix_c H, ElInt nx, ElInt ny, complex_float omega, ElInt numPmlPoints, float sigma, float pmlExp)

ElError ElHelmholtzPML2DDist_z(ElDistMatrix_z H, ElInt nx, ElInt ny, complex_double omega, ElInt numPmlPoints, double sigma, double pmlExp)

2D Helmholtz

ElError ElHelmholtzPML3D_c(ElMatrix_c H, ElInt nx, ElInt ny, ElInt nz, complex_float omega, ElInt numPmlPoints, float sigma, float pmlExp)

ElError ElHelmholtzPML3D_z(ElMatrix_z H, ElInt nx, ElInt ny, ElInt nz, complex_double omega, ElInt numPmlPoints, double sigma, double pmlExp)

ElError ElHelmholtzPML3DDist_c(ElDistMatrix_c H, ElInt nx, ElInt ny, ElInt nz, complex_float omega, ElInt numPmlPoints, float sigma, float pmlExp)

ElError ElHelmholtzPML3DDist_z(ElDistMatrix_z H, ElInt nx, ElInt ny, ElInt nz, complex_double omega, ElInt numPmlPoints, double sigma, double pmlExp)

3D Helmholtz

Python API

HelmholtzPML1D(H, nx, omega, numPmlPoints, sigma, pmlExp)

HelmholtzPML2D(H, nx, ny, omega, numPmlPoints, sigma, pmlExp)

HelmholtzPML3D(H, nx, ny, nz, omega, numPmlPoints, sigma, pmlExp)