A Method of Smooth Bivariate Interpolation for Data Given on a Generalized Curvilinear Grid. - David W. Zingg; Maurice Yarrow (SIAM J. Sci. Comput., 1992)

High-Accuracy Finite-Difference Schemes for Linear Wave Propagation. - David W. Zingg; Harvard Lomax; Henry M. Jurgens (SIAM J. Sci. Comput., 1996)

Comparison of High-Accuracy Finite-Difference Methods for Linear Wave Propagation. - David W. Zingg (SIAM J. Sci. Comput., 2000)

Numerical Solution of the Time-Domain Maxwell Equations Using High-Accuracy Finite-Difference Methods. - Henry M. Jurgens; David W. Zingg (SIAM J. Sci. Comput., 2001)

A Jacobian-free Newton-Krylov algorithm for compressible turbulent fluid flows. - Todd T. Chisholm; David W. Zingg (J. Comput. Phys., 2009)

A Simplified and Flexible Variant of GCROT for Solving Nonsymmetric Linear Systems. - Jason E. Hicken; David W. Zingg (SIAM J. Sci. Comput., 2010)

Superconvergent Functional Estimates from Summation-By-Parts Finite-Difference Discretizations. - Jason E. Hicken; David W. Zingg (SIAM J. Sci. Comput., 2011)

Summation-by-parts operators and high-order quadrature. - Jason E. Hicken; David W. Zingg (J. Comput. Appl. Math., 2013)

Generalized Summation-by-Parts Operators for the Second Derivative with Variable Coefficients. - David C. Del Rey Fernández; David W. Zingg (CoRR, 2014)

A generalized framework for nodal first derivative summation-by-parts operators. - David C. Del Rey Fernández; Pieter D. Boom; David W. Zingg (J. Comput. Phys., 2014)

Dual consistency and functional accuracy: a finite-difference perspective. - Jason E. Hicken; David W. Zingg (J. Comput. Phys., 2014)

High-Order Implicit Time-Marching Methods Based on Generalized Summation-By-Parts Operators. - Pieter D. Boom; David W. Zingg (SIAM J. Sci. Comput., 2015)

Generalized Summation-by-Parts Operators for the Second Derivative. - David C. Del Rey Fernández; David W. Zingg (SIAM J. Sci. Comput., 2015)

Efficient numerical differentiation of implicitly-defined curves for sparse systems. - David A. Brown; David W. Zingg (J. Comput. Appl. Math., 2016)

A monolithic homotopy continuation algorithm with application to computational fluid dynamics. - David A. Brown; David W. Zingg (J. Comput. Phys., 2016)

Multidimensional Summation-by-Parts Operators: General Theory and Application to Simplex Elements. - Jason E. Hicken; David C. Del Rey Fernández; David W. Zingg (SIAM J. Sci. Comput., 2016)

Corner-corrected diagonal-norm summation-by-parts operators for the first derivative with increased order of accuracy. - David C. Del Rey Fernández; Pieter D. Boom; David W. Zingg (J. Comput. Phys., 2017)

Optimization of high-order diagonally-implicit Runge-Kutta methods. - Pieter D. Boom; David W. Zingg (J. Comput. Phys., 2018)

Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements. - Jared Crean; Jason E. Hicken; David C. Del Rey Fernández; David W. Zingg; Mark H. Carpenter (J. Comput. Phys., 2018)

Simultaneous Approximation Terms for Multi-dimensional Summation-by-Parts Operators. - David C. Del Rey Fernández; Jason E. Hicken; David W. Zingg (J. Sci. Comput., 2018)

Conservative and Stable Degree Preserving SBP Operators for Non-conforming Meshes. - Lucas Friedrich; David C. Del Rey Fernández; Andrew R. Winters; Gregor J. Gassner; David W. Zingg; Jason E. Hicken (J. Sci. Comput., 2018)

Matrix-free monolithic homotopy continuation with application to computational aerodynamics. - David A. Brown; David W. Zingg (Numer. Algorithms, 2018)

Monolithic homotopy continuation with predictor based on higher derivatives. - David A. Brown; David W. Zingg (J. Comput. Appl. Math., 2019)

Extension of Tensor-Product Generalized and Dense-Norm Summation-by-Parts Operators to Curvilinear Coordinates. - David C. Del Rey Fernández; Pieter D. Boom; Mark H. Carpenter; David W. Zingg (J. Sci. Comput., 2019)

Optimization of multidimensional diagonal-norm summation-by-parts operators on simplices. - André L. Marchildon; David W. Zingg (J. Comput. Phys., 2020)

Superconvergent Functional Estimates from Tensor-Product Generalized Summation-by-Parts Discretizations in Curvilinear Coordinates. - David A. Craig Penner; David W. Zingg (J. Sci. Comput., 2020)

Entropy-Stable Multidimensional Summation-by-Parts Discretizations on hp-Adaptive Curvilinear Grids for Hyperbolic Conservation Laws. - Siavosh Shadpey; David W. Zingg (J. Sci. Comput., 2020)

Simultaneous approximation terms and functional accuracy for diffusion problems discretized with multidimensional summation-by-parts operators. - Zelalem Arega Worku; David W. Zingg (J. Comput. Phys., 2021)

Unisolvency for Polynomial Interpolation in Simplices with Symmetrical Nodal Distributions. - André L. Marchildon; David W. Zingg (J. Sci. Comput., 2022)

A Unifying Algebraic Framework for Discontinuous Galerkin and Flux Reconstruction Methods Based on the Summation-by-Parts Property. - Tristan Montoya; David W. Zingg (J. Sci. Comput., 2022)

Accurate High-Order Tensor-Product Generalized Summation-By-Parts Discretizations of Hyperbolic Conservation Laws: General Curved Domains and Functional Superconvergence. - David A. Craig Penner; David W. Zingg (J. Sci. Comput., 2022)

Stability and Functional Superconvergence of Narrow-Stencil Second-Derivative Generalized Summation-By-Parts Discretizations. - Zelalem Arega Worku; David W. Zingg (J. Sci. Comput., 2022)

Entropy-split multidimensional summation-by-parts discretization of the Euler and Navier-Stokes equations. - Zelalem Arega Worku; David W. Zingg (CoRR, 2023)

Efficient Entropy-Stable Discontinuous Spectral-Element Methods Using Tensor-Product Summation-by-Parts Operators on Triangles and Tetrahedra. - Tristan Montoya; David W. Zingg (CoRR, 2023)

A Non-intrusive Solution to the Ill-Conditioning Problem of the Gradient-Enhanced Gaussian Covariance Matrix for Gaussian Processes. - André L. Marchildon; David W. Zingg (J. Sci. Comput., 2023)

Entropy-split multidimensional summation-by-parts discretization of the Euler and compressible Navier-Stokes equations. - Zelalem Arega Worku; David W. Zingg (J. Comput. Phys., 2024)

Efficient Tensor-Product Spectral-Element Operators with the Summation-by-Parts Property on Curved Triangles and Tetrahedra. - Tristan Montoya; David W. Zingg (SIAM J. Sci. Comput., 2024)

Quadrature Rules on Triangles and Tetrahedra for Multidimensional Summation-By-Parts Operators. - Zelalem Arega Worku; Jason E. Hicken; David W. Zingg (J. Sci. Comput., 2024)

Tensor-product split-simplex summation-by-parts operators. - Zelalem Arega Worku; Jason E. Hicken; David W. Zingg (J. Comput. Phys., 2025)

Relative Efficiency of Finite-Difference and Discontinuous Spectral-Element Summation-by-Parts Methods on Distorted Meshes. - Pieter D. Boom; David C. Del Rey Fernández; David W. Zingg (J. Sci. Comput., 2025)

Stable Volume Dissipation for High-Order Finite-Difference Methods with the Generalized Summation-by-Parts Property. - Alex Bercik; David A. Craig Penner; David W. Zingg (CoRR, 2025)

Very high-order symmetric positive-interior quadrature rules on triangles and tetrahedra. - Zelalem Arega Worku; Jason E. Hicken; David W. Zingg (J. Comput. Appl. Math., 2026)