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] The mimetic finite difference method for elliptic problems
This book describes the theoretical and computational aspects of the mimetic finite
difference method for a wide class of multidimensional elliptic problems, which includes …
difference method for a wide class of multidimensional elliptic problems, which includes …
Mimetic finite difference method
The mimetic finite difference (MFD) method mimics fundamental properties of mathematical
and physical systems including conservation laws, symmetry and positivity of solutions …
and physical systems including conservation laws, symmetry and positivity of solutions …
Large calculation of the flow over a hypersonic vehicle using a GPU
Graphics processing units are capable of impressive computing performance up to
518Gflops peak performance. Various groups have been using these processors for general …
518Gflops peak performance. Various groups have been using these processors for general …
A stable high-order finite difference scheme for the compressible Navier–Stokes equations, far-field boundary conditions
We construct a stable high-order finite difference scheme for the compressible Navier–
Stokes equations, that satisfy an energy estimate. The equations are discretized with high …
Stokes equations, that satisfy an energy estimate. The equations are discretized with high …
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 …
Multidimensional summation-by-parts operators: general theory and application to simplex elements
Summation-by-parts (SBP) finite-difference discretizations share many attractive properties
with Galerkin finite-element methods (FEMs), including time stability and superconvergent …
with Galerkin finite-element methods (FEMs), including time stability and superconvergent …
A stable high-order finite difference scheme for the compressible Navier–Stokes equations: no-slip wall boundary conditions
M Svärd, J Nordström - Journal of Computational Physics, 2008 - Elsevier
A stable wall boundary procedure is derived for the discretized compressible Navier–Stokes
equations. The procedure leads to an energy estimate for the linearized equations. We …
equations. The procedure leads to an energy estimate for the linearized equations. We …