122 citations · 230 across the 20 of their papers we have counts for
22 papers
Targeted Entropy-Stable Nonlinear Artificial Dissipation for High-Order Spectral-Element Summation-By-Parts Discretizations
Zelalem Arega Worku, Alex Bercik, David C. Del Rey Fernández +1
Artificial dissipation improves the robustness of high-order methods for under-resolved flows, but can compromise accuracy and suppress physically relevant structures if its streng…
Construction and Optimization of Summation-by-Parts Operators for General Function Spaces Using an Improved Generalized Gaussian Quadrature Algorithm
Alex Bercik, Lisa Patrascu, David W. Zingg
We construct optimized summation-by-parts (SBP) operators for general function spaces with provably minimal degrees of freedom on open, closed, and half-open nodal distributions. T…
On the Practical Impact of Local Linear Instabilities in Entropy-Stable Schemes
Alex Bercik, David W. Zingg
Local linear instability refers to the linearized discrete operator exhibiting perturbation growth exceeding that of the corresponding continuous linearized problem. In the context…
Convergence of entropy-stable continuous summation-by-parts discretizations of symmetric hyperbolic conservation laws
Zelalem Arega Worku, David C. Del Rey Fernández, David W. Zingg
The Lax equivalence theorem guarantees convergence of stable and consistent discretizations for linear hyperbolic partial differential equations (PDEs). For nonlinear problems, how…
Stable Volume Dissipation for High-Order Finite-Difference and Spectral-Element Methods with the Summation-by-Parts Property
Alex Bercik, David A. Craig Penner, David W. Zingg
The construction of stable, conservative, and accurate volume dissipation is extended to discretizations that possess a generalized summation-by-parts (SBP) property within a tenso…
Very high-order symmetric positive-interior quadrature rules on triangles and tetrahedra
Zelalem Arega Worku, Jason E. Hicken, David W. Zingg
We present novel fully-symmetric quadrature rules with positive weights and strictly interior nodes of degrees up to 84 on triangles and 40 on tetrahedra. Initial guesses for solvi…
Tensor-Product Split-Simplex Summation-By-Parts Operators
Zelalem Arega Worku, Jason E. Hicken, David W. Zingg
We present an approach to construct efficient sparse summation-by-parts (SBP) operators on triangles and tetrahedra with a tensor-product structure. The operators are constructed b…
Efficient Entropy-Stable Discontinuous Spectral-Element Methods Using Tensor-Product Summation-by-Parts Operators on Triangles and Tetrahedra
Tristan Montoya, David W. Zingg
We present a new class of efficient and robust discontinuous spectral-element methods of arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular…
Quadrature Rules on Triangles and Tetrahedra for Multidimensional Summation-By-Parts Operators
Zelalem Arega Worku, Jason E. Hicken, David W. Zingg
Multidimensional diagonal-norm summation-by-parts (SBP) operators with collocated volume and facet nodes, known as diagonal- operators, are attractive for entropy-sta…
A Solution to the Ill-Conditioning of Gradient-Enhanced Covariance Matrices for Gaussian Processes
André L. Marchildon, David W. Zingg
Gaussian processes provide probabilistic surrogates for various applications including classification, uncertainty quantification, and optimization. Using a gradient-enhanced covar…
Efficient Tensor-Product Spectral-Element Operators with the Summation-by-Parts Property on Curved Triangles and Tetrahedra
Tristan Montoya, David W. Zingg
We present an extension of the summation-by-parts (SBP) framework to tensor-product spectral-element operators in collapsed coordinates. The proposed approach enables the construct…
Entropy-split multidimensional summation-by-parts discretization of the Euler and compressible Navier-Stokes equations
Zelalem Arega Worku, David W. Zingg
High-order Hadamard-form entropy stable multidimensional summation-by-parts discretizations of the Euler and compressible Navier-Stokes equations are considerably more expensive th…
Stability and Functional Superconvergence of Narrow-Stencil Second-Derivative Generalized Summation-By-Parts Discretizations
Zelalem Arega Worku, David W. Zingg
We analyze the stability and functional superconvergence of discretizations of diffusion problems with the narrow-stencil second-derivative generalized summation-by-parts (SBP) ope…
A unifying algebraic framework for discontinuous Galerkin and flux reconstruction methods based on the summation-by-parts property
Tristan Montoya, David W. Zingg
We propose a unifying framework for the matrix-based formulation and analysis of discontinuous Galerkin (DG) and flux reconstruction (FR) methods for conservation laws on general u…
Simultaneous approximation terms and functional accuracy for diffusion problems discretized with multidimensional summation-by-parts operators
Zelalem Arega Worku, David W. Zingg
Several types of simultaneous approximation term (SAT) for diffusion problems discretized with diagonal-norm multidimensional summation-by-parts (SBP) operators are analyzed based…
Conservative and Stable Degree Preserving SBP Operators for Non-Conforming Meshes
Lucas Friedrich, David C. Del Rey Fernandez, Andrew R. Winters +3
Non-conforming numerical approximations offer increased flexibility for applications that require high resolution in a localized area of the computational domain or near complex ge…
Simultaneous Approximation Terms for Multi-Dimensional Summation-by-Parts Operators
David C. Del Rey Fernández, Jason E. Hicken, David W. Zingg
This paper is concerned with the accurate, conservative, and stable imposition of boundary conditions and inter-element coupling for multi-dimensional summation-by-parts (SBP) fini…
Multidimensional Summation-By-Parts Operators: General Theory and Application to Simplex Elements
Jason E. Hicken, David C. Del Rey Fernández, David W. Zingg
Summation-by-parts (SBP) finite-difference discretizations share many attractive properties with Galerkin finite-element methods (FEMs), including time stability and superconvergen…
Generalized Summation-by-Parts Operators for the Second Derivative with Variable Coefficients
David C. Del Rey Fernández, David W. Zingg
The comprehensive generalization of summation-by-parts of Del Rey Fernández et al.\ (J. Comput. Phys., 266, 2014) is extended to approximations of second derivatives with variable…
Runge-Kutta Characterization of the Generalized Summation-by-Parts Approach in Time
Pieter D. Boom, David W. Zingg
This article extends the theory of dual-consistent summation-by-parts (SBP) and generalized SBP (GSBP) time-marching methods by showing that they are implicit Runge-Kutta schemes.…
High-Order Implicit Time-Marching Methods Based on Generalized Summation-By-Parts Operators
Pieter D. Boom, David W. Zingg
This article extends the theory of classical finite-difference summation-by-parts (FD-SBP) time-marching methods to the generalized summation-by-parts (GSBP) framework. Dual-consis…
Summation-By-Parts Operators and High-Order Quadrature
Jason E. Hicken, David W. Zingg
Summation-by-parts (SBP) operators are finite-difference operators that mimic integration by parts. This property can be useful in constructing energy-stable discretizations of par…