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math.NA2023
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…
math.NA2023
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…
math.OC2023
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…