Using multifrontal hierarchically solver and HPC systems for 3D Helmholtz problem

We present a multi-frontal hierarchically semi-separable solver to perform forward modeling of the 3D Helmholtz acoustic problem. Our frequency-domain solver combines two efficient approaches. First, it uses an optimal 27-point finite-difference scheme to decrease numerical dispersion and reduce required discretization of the model in terms of points per wavelength from 15 to about 4. Second, it uses a supernodal multi-frontal method based on low-rank approximation and hierarchically semi-separable (HSS) structure to improve performance, decrease memory usage and make it practical for realistic size 3D models required by full-waveform inversion. We performed validation and performance testing our new solver using a 3D synthetic model. Performance and OMP scalability of the solver were compared with the Intel MKL PARDISO.