arXiv subjects

Kenny Wiratama

Publications and source records attributed to Kenny Wiratama.

3 recordsLinked to original sources

arXiv2026

A space-time dual-pairing summation-by-parts framework for forward and adjoint wave equations

In this paper, we propose the first of its kind space-time dual-pairing summation by parts (DP-SBP) numerical framework for forward and adjoint wave propagation problems. This novel approach enables us to achieve spatial and temporal high order accuracy while naturally introducing dissipation in time. Within this framework, initial and boundary conditions are weakly imposed using the simultaneous approximation term (SAT) technique. Fully discrete energy estimates are derived, ensuring the stability of the resulting numerical scheme. Furthermore, the proposed space-time numerical framework allows us to construct adjoint consistent fully discrete numerical approximations, which can be applied to solve inverse wave propagation problems. We provide numerical experiments in one and two spatial dimensions to verify the theoretical analysis and demonstrate convergence of numerical errors.

math.NA↗

arXiv2023

Well-posed boundary conditions and energy stable discontinuous Galerkin spectral element method for the linearized Serre equations

We derive well-posed boundary conditions for the linearized Serre equations in one spatial dimension by utilizing the energy method. An energy stable and conservative discontinuous Galerkin spectral element method with simple upwind numerical fluxes is proposed for solving the initial boundary value problem. We derive discrete energy estimates for the numerical approximation and prove a priori error estimates in the energy norm. Detailed numerical examples are provided to verify the theoretical analysis and show convergence of numerical errors.

math.NA↗

arXiv2021

A conservative and energy stable discontinuous spectral element method for the shifted wave equation in second order form

In this paper, we develop a provably energy stable and conservative discontinuous spectral element method for the shifted wave equation in second order form. The proposed method combines the advantages and central ideas of very successful numerical techniques, the summation-by-parts finite difference method, the spectral method and the discontinuous Galerkin method. We prove energy-stability, discrete conservation principle, and derive error estimates in the energy norm for the (1+1)-dimensions shifted wave equation in second order form. The energy-stability results, discrete conservation principle, and the error estimates generalise to multiple dimensions using tensor products of quadrilateral and hexahedral elements. Numerical experiments, in (1+1)-dimensions and (2+1)-dimensions, verify the theoretical results and demonstrate optimal convergence of $L^2$ numerical errors at subsonic, sonic and supersonic regimes.

math.NA↗