Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
Abstract Summation-by-parts (SBP) operators have a number of properties that make them
an attractive option for higher-order spatial discretizations of partial differential equations. In …
an attractive option for higher-order spatial discretizations of partial differential equations. In …
[HTML][HTML] Continuum and discrete initial-boundary value problems and Einstein's field equations
Many evolution problems in physics are described by partial differential equations on an
infinite domain; therefore, one is interested in the solutions to such problems for a given …
infinite domain; therefore, one is interested in the solutions to such problems for a given …
Review of summation-by-parts schemes for initial–boundary-value problems
M Svärd, J Nordström - Journal of Computational Physics, 2014 - Elsevier
High-order finite difference methods are efficient, easy to program, scale well in multiple
dimensions and can be modified locally for various reasons (such as shock treatment for …
dimensions and can be modified locally for various reasons (such as shock treatment for …
[图书][B] Time dependent problems and difference methods
B Gustafsson, HO Kreiss, J Oliger - 1995 - books.google.com
Time dependent problems frequently pose challenges in areas of science and engineering
dealing with numerical analysis, scientific computation, mathematical models, and most …
dealing with numerical analysis, scientific computation, mathematical models, and most …
Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: Theory and boundary conditions
The Lax–Wendroff theorem stipulates that a discretely conservative operator is necessary to
accurately capture discontinuities. The discrete operator, however, need not be derived from …
accurately capture discontinuities. The discrete operator, however, need not be derived from …
Summation by parts operators for finite difference approximations of second-derivatives with variable coefficients
K Mattsson - Journal of Scientific Computing, 2012 - Springer
Finite difference operators approximating second derivatives with variable coefficients and
satisfying a summation-by-parts rule have been derived for the second-, fourth-and sixth …
satisfying a summation-by-parts rule have been derived for the second-, fourth-and sixth …
An Entropy Stable h / p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property
L Friedrich, AR Winters, DC Del Rey Fernández… - Journal of Scientific …, 2018 - Springer
This work presents an entropy stable discontinuous Galerkin (DG) spectral element
approximation for systems of non-linear conservation laws with general geometric (h) and …
approximation for systems of non-linear conservation laws with general geometric (h) and …
High-order L2 stable multi-domain finite difference method for compressible flows
TC Fisher - 2012 - search.proquest.com
Computational fluid dynamics can be used to gain deeper insight into compressible flow
physics, but current limitations in numerical methods, computing hardware, data analysis …
physics, but current limitations in numerical methods, computing hardware, data analysis …
High order finite difference methods for the wave equation with non-conforming grid interfaces
S Wang, K Virta, G Kreiss - Journal of Scientific Computing, 2016 - Springer
We use high order finite difference methods to solve the wave equation in the second order
form. The spatial discretization is performed by finite difference operators satisfying a …
form. The spatial discretization is performed by finite difference operators satisfying a …
An SBP-SAT FDTD subgridding method using staggered Yee's grids without modifying field components for TM analysis
A summation-by-parts simultaneous approximation term (SBP-SAT) finite-difference time-
domain (FDTD) subgridding method is proposed to model geometrically fine structures in …
domain (FDTD) subgridding method is proposed to model geometrically fine structures in …