An efficient ADER-DG local time stepping scheme for 3D HPC simulation of seismic waves in poroelastic media

Many applications from geosciences require simulations of seismic waves in porous media. Biot's theory poroelasticity describes the coupling between solid and fluid phases introduces a stiff source term, thereby increasing computational cost motivating efficient methods utilising High-Performance Computing. We present novel realisation discontinuous Galerkin scheme with Arbitrary DERivative time stepping (ADER-DG) that copes terms. To integrate this term reasonable step size, we use an element-local space-time predictor, which needs to solve medium-sized linear systems - 1000 10000 unknowns each element update (i.e., billions times). block-wise back-substitution algorithm for solving these efficiently. In comparison LU decomposition, reduce number floating-point operations by factor up 25. The is mapped sequence small matrix-matrix multiplications, code generators are available generate highly optimised code. verify new solver thoroughly problems complexity. demonstrate high-order convergence 3D problems. correct treatment point sources, material interfaces traction-free boundary conditions. addition, compare against finite difference newly defined layer over half-space problem. find extremely high accuracy required resolve slow P-wave at free surface, while particle velocities not affected coarser resolutions. By using clustered local scheme, solution 6 10 compared global stepping. conclude our study scaling performance analysis, demonstrating implementation's efficiency its potential extreme-scale simulations.