Brown's research interests include scalable solvers for implicit multiphysics, high order PDE discretization in complex geometry, compatible discretizations for heterogeneous flows, and PDE-constrained optimization. His work emphasizes robust and high performance parallel software, often relating to PETSc.
keywords
multilevel solvers, simulation and analysis of PDE systems, parallel algorithms and software, computational fluid dynamics, geodynamics, glaciology, structural mechanics, uncertainty quantification, experimental design
APPM 6950 - Master's Thesis
Primary Instructor
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Fall 2020 / Spring 2021
May be repeated up to 6 total credit hours.
CSCI 3656 - Numerical Computation
Primary Instructor
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Spring 2018 / Spring 2019 / Spring 2020 / Spring 2021 / Spring 2022 / Spring 2023
Covers development, computer implementation, and analysis of numerical methods for applied mathematical problems. Explores topics such as floating point arithmetic, numerical solution of linear systems of equations, root finding, numerical interpolation, differentiation, and integration.
CSCI 4576 - High-Performance Scientific Computing
Primary Instructor
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Fall 2019
Introduces computing systems, software and methods used to solve large-scale problems in science and engineering. Students use high-performance workstations and a supercomputer. Recommended prerequisite: APPM 4650 or CSCI 3656 or MATH 4650 or MCEN 3030. Same as CSCI 5576.
CSCI 4950 - Senior Thesis
Primary Instructor
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Fall 2018 / Spring 2019 / Spring 2022 / Spring 2024
Provides an opportunity for senior computer science majors to conduct exploratory research in computer science. Department enforced restriction, successful completion of a minimum of 36 credit hours of Computer Science coursework and approved WRTG. May be repeated up to 8 total credit hours.
CSCI 5576 - High-Performance Scientific Computing
Primary Instructor
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Fall 2019
Introduces computing systems, software and methods used to solve large-scale problems in science and engineering. Students use high-performance workstations and a supercomputer. First course in a two-semester sequence. Same as CSCI 4576.
CSCI 5606 - Principles of Numerical Computation
Primary Instructor
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Spring 2023
Highlights computer arithmetic, solution of linear systems, least-squares approximations, nonlinear algebraic equations, interpolation, and quadrature. Recommended prerequisites: CSCI 3656 and three semesters of calculus or equivalent.
CSCI 5636 - Numerical Solution of Partial Differential Equations
Primary Instructor
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Fall 2018 / Fall 2021 / Fall 2022 / Fall 2023
Focuses on discretization techniques such as finite difference, finite element and finite volume methods, and parallel solution algorithms such as Krylov subspace methods, domain decomposition and multilevel methods.
