Harmonic coordinate finite element method for acoustic waves
William W. Symes, Xin Wang · 2012
The 2D harmonic coordinate finite element method (HCFEM) achieves optimal second-order convergence for static and dynamic acoustic boundary value problems problems with spatially heterogeneous bulk modulus and density, at the additional cost of solving two auxiliary elliptic boundary value problems. Unlike the conventional finite element method (FEM), HCFEM does not require interface-conforming meshes to achieve optimal convergence rate. HCFEM stiffness and mass matrices are constructed in a systematic procedure, and have the same sparsity pattern as those in the standard regular grid FEM. Mass-lumping in HCFEM is proved to preserve the optimal convergence order, due to the smoothness of acoustic solutions in harmonic coordinates, and results in an efficient, explicit time step.