[HTML][HTML] Boundary-optimized summation-by-parts operators for finite difference approximations of second derivatives with variable coefficients

V Stiernström, M Almquist, K Mattsson - Journal of Computational Physics, 2023 - Elsevier
Boundary-optimized summation-by-parts (SBP) finite difference operators for second
derivatives with variable coefficients are presented. The operators achieve increased …

A broad class of conservative numerical methods for dispersive wave equations

H Ranocha, D Mitsotakis, DI Ketcheson - arxiv preprint arxiv:2006.14802, 2020 - arxiv.org
We develop a general framework for designing conservative numerical methods based on
summation by parts operators and split forms in space, combined with relaxation Runge …

[PDF][PDF] SummationByPartsOperators. jl: A Julia library of provably stable discretization techniques with mimetic properties

H Ranocha - Journal of Open Source Software, 2021 - joss.theoj.org
SummationByPartsOperators. jl is a Julia library of summation-by-parts (SBP) operators,
which are discrete derivative operators developed to get provably stable (semi-) …

[HTML][HTML] Adjoint-based inversion for stress and frictional parameters in earthquake modeling

V Stiernström, M Almquist, EM Dunham - Journal of Computational Physics, 2024 - Elsevier
We present an adjoint-based optimization method to invert for stress and frictional
parameters used in earthquake modeling. The forward problem is linear elastodynamics …

[HTML][HTML] SBP–SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids

L Gao, DCDR Fernández, M Carpenter… - Journal of Computational …, 2019 - Elsevier
We consider the numerical simulation of the acoustic wave equations arising from seismic
applications, for which staggered grid finite difference methods are popular choices due to …

Discrete vector calculus and Helmholtz Hodge decomposition for classical finite difference summation by parts operators

H Ranocha, K Ostaszewski, P Heinisch - Communications on Applied …, 2020 - Springer
In this article, discrete variants of several results from vector calculus are studied for classical
finite difference summation by parts operators in two and three space dimensions. It is …

Non-conforming interface conditions for the second-order wave equation

G Eriksson - Journal of Scientific Computing, 2023 - Springer
Imposition methods of interface conditions for the second-order wave equation with non-
conforming grids is considered. The spatial discretization is based on high order finite …

Weak versus strong wall boundary conditions for the incompressible Navier-Stokes equations

G Eriksson, K Mattsson - Journal of Scientific Computing, 2022 - Springer
The pressure-velocity formulation of the incompressible Navier-Stokes equations is solved
using high-order finite difference operators satisfying a summation-by-parts property. Two …

Relative Efficiency of Finite-Difference and Discontinuous Spectral-Element Summation-by-Parts Methods on Distorted Meshes

PD Boom, DC Del Rey Fernández… - Journal of Scientific …, 2025 - Springer
Conventional wisdom suggests that high-order finite-difference methods are more efficient
than high-order discontinuous spectral-element methods on smooth meshes, but less …

Efficient discretization of the Laplacian on complex geometries

G Eriksson - arxiv preprint arxiv:2404.09050, 2024 - arxiv.org
Highly accurate simulations of problems including second derivatives on complex
geometries are of primary interest in academia and industry. Consider for example the …