Hybridized Summation-by-Parts Finite Difference Methods

  title={Hybridized Summation-by-Parts Finite Difference Methods},
  author={Jeremy E. Kozdon and Brittany A. Erickson and Lucas C. Wilcox},
  journal={Journal of Scientific Computing},
We present a hybridization technique for summation-by-parts finite difference methods with weak enforcement of interface and boundary conditions for second order, linear elliptic partial differential equations. The method is based on techniques from the hybridized discontinuous Galerkin literature where local and global problems are defined for the volume and trace grid points, respectively. By using a Schur complement technique the volume points can be eliminated, which drastically reduces the… 
1 Citations

Incorporating Full Elastodynamic Effects and Dipping Fault Geometries in Community Code Verification Exercises for Simulations of Earthquake Sequences and Aseismic Slip (SEAS)

Numerical modeling of earthquake dynamics and derived insight for seismic hazard relies on credible, reproducible model results. The sequences of earthquakes and aseismic slip (SEAS) initiative has



High Order Finite Difference Methods for the Wave Equation with Non-conforming Grid Interfaces

By imposing an additional constraint on the interface operators, an energy estimate of the numerical scheme for the second order wave equation is derived and eigenvalue analyses are carried out to investigate the additional constraint and its relation to stability.

Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes

Abstract We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for

High Order Stable Finite Difference Methods for the Schrödinger Equation

It is shown that a boundary closure of the numerical approximations ofOrder m lead to global accuracy of order m+2, and the results are supported by numerical simulations.

Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients

  • K. Mattsson
  • Mathematics
    Journal of Scientific Computing
  • 2011
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-order case by

A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy

Stable and accurate interface conditions based on the SAT penalty method are derived for the linear advection?diffusion equation. The conditions are functionally independent of the spatial order of

Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems

A unifying framework for hybridization of finite element methods for second order elliptic problems is introduced, thanks to which it is possible to see how to devise novel methods displaying very localized and simple mortaring techniques, as well as methods permitting an even further reduction of the number of globally coupled degrees of freedom.

Stable and accurate second-order formulation of the shifted wave equation

High order finite difference approximations are derived for a onedimensional model of the shifted wave equation written in second-order form. The domain is discretized using fully compatible

Stable Boundary Treatment for the Wave Equation on Second-Order Form

A stable and accurate boundary treatment is derived for the second-order wave equation using narrow-diagonal summation by parts operators and the boundary conditions are imposed using a penalty method, leading to fully explicit time integration.

Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods

Block-to-block interface interpolation operators are constructed for several common high-order finite difference discretizations that maintain the strict stability, accuracy, and conservation properties of the base scheme even when nonconforming grids or dissimilar operators are used in adjoining blocks.