Journal Articles

Efficient Tensor-Product Spectral-Element Operators with the Summation-by-Parts Property on Curved Triangles and Tetrahedra
Tristan Montoya and David W. Zingg
SIAM Journal on Scientific Computing, 2024

Efficient Entropy-Stable Discontinuous Spectral-Element Methods Using Tensor-Product Summation-by-Parts Operators on Triangles and Tetrahedra
Tristan Montoya and David W. Zingg
Journal of Computational Physics, 2024

A Unifying Algebraic Framework for Discontinuous Galerkin and Flux Reconstruction Methods Based on the Summation-by-Parts Property
Tristan Montoya and David W. Zingg
Journal of Scientific Computing, 2022

Conference Proceedings

Stable and Conservative High-Order Methods on Triangular Elements Using Tensor-Product Summation-By-Parts Operators (Awarded Best Student Paper)
Tristan Montoya and David W. Zingg
International Conference on Computational Fluid Dynamics, 2022

Thesis

Provably Stable Discontinuous Spectral-Element Methods with the Summation-by-Parts Property: Unified Matrix Analysis and Efficient Tensor-Product Formulations on Curved Simplices
Tristan Montoya
University of Toronto, 2024