My research features the development of: 1. Fast algorithmic frameworks for large-scale physics simulation 2. Fast direct solvers and hierarchical decomposition methods 3. Scientific data compression methods 4. Integral equation formulations for numerical PDE in fluids, active soft matter, biophysics, wave scattering, elasticity. 5. Singular and near-singular integration methods for integral kernels 6. Modeling and fast simulation frameworks for heterogeneous power grid systems.
keywords
Integral Equations, Fast Algorithms, Fast Multipole Methods, Randomized Algorithms, Tensor Decomposition, Numerical PDE, Computational soft matter, Biophysics and materials simulation, Fast algorithms for power systems
APPM 1360 - Calculus 2 for Engineers
Primary Instructor
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Spring 2022
Continuation of APPM 1350. Focuses on applications of the definite integral, methods of integration, improper integrals, Taylor's theorem, and infinite series. Degree credit not granted for this course and MATH 2300.
APPM 4600 - Numerical Methods and Scientific Computing
Primary Instructor
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Spring 2023 / Spring 2024 / Fall 2024
Provides an introduction to numerical analysis and scientific computing. Numerical analysis topics include root finding, interpolation, quadrature, linear system solution techniques, and techniques for approximating eigenvalues. Scientific computing topics include code development and repository management in addition to an introduction to shared and distributed memory computing. Involves hands-on learning with weekly group interactions and a final project including a report and in-class presentation. Recommended prerequisite: knowledge of a programming language such as Python, and C++.
APPM 4650 - Intermediate Numerical Analysis 1
Primary Instructor
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Fall 2021 / Spring 2022
Focuses on numerical solution of nonlinear equations, interpolation, methods in numerical integration, numerical solution of linear systems, and matrix eigenvalue problems. Stresses significant computer applications and software. Department enforced prerequisite: knowledge of a programming language. Same as MATH 4650.
APPM 5600 - Numerical Analysis 1
Primary Instructor
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Fall 2022
Solution of nonlinear algebraic equations, interpolation, integration, approximation, and numerical linear algebra. Department enforced prerequisite: APPM 3310 or MATH 2130 and experience with a scientific programming language.
APPM 5610 - Numerical Analysis 2
Primary Instructor
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Spring 2023
Numerical linear algebra, eigenvalue problems, optimization problems, and ordinary and partial differential equations. Department enforced prerequisite: APPM 5600 or MATH 5600.
MATH 4650 - Intermediate Numerical Analysis 1
Primary Instructor
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Fall 2021
Focuses on numerical solution of nonlinear equations, interpolation, methods in numerical integration, numerical solution of linear systems, and matrix eigenvalue problems. Stresses significant computer applications and software. Department enforced prerequisite: knowledge of a programming language. Same as APPM 4650.
MATH 5600 - Numerical Analysis 1
Primary Instructor
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Fall 2022
Solution of nonlinear algebraic equations, interpolation, approximation theory and numerical integration. Department enforced prerequisites: MATH 2130 or MATH 2135 or APPM 3310 and experience with a scientific programming language. Instructor consent required for undergraduates.
