[HTML][HTML] Boundary-optimized summation-by-parts operators for finite difference approximations of second derivatives with variable coefficients
Boundary-optimized summation-by-parts (SBP) finite difference operators for second
derivatives with variable coefficients are presented. The operators achieve increased …
derivatives with variable coefficients are presented. The operators achieve increased …
A broad class of conservative numerical methods for dispersive wave equations
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 …
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-) …
which are discrete derivative operators developed to get provably stable (semi-) …
[HTML][HTML] Adjoint-based inversion for stress and frictional parameters in earthquake modeling
We present an adjoint-based optimization method to invert for stress and frictional
parameters used in earthquake modeling. The forward problem is linear elastodynamics …
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
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 …
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
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 …
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 …
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 …
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
Conventional wisdom suggests that high-order finite-difference methods are more efficient
than high-order discontinuous spectral-element methods on smooth meshes, but less …
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 …
geometries are of primary interest in academia and industry. Consider for example the …