University of Washington · Applied Mathematics

Higher Order Methods, etc.

A research group at the University of Washington exploring the frontiers of mathematical higher order methods, from ... to ....

About the Group

The Higher Order Methods, etc. research group (HOME) meets once a week to discuss developments in higher order methods from both an applied and theoretical perspective.

Discussions center around specific topics including acoustic scattering, low rank structures, hierarchical methods, rational approximations, pseudospectra in matrix pencils

UW student may reach out if they are interested in attending.

Department Applied Mathematics, University of Washington
Meeting Frequency Once a week during the academic quarters
Topics of Study
  • PDE Solvers for Wave Scattering
  • Hierarchical Methods for Optimization
  • Rational Approximation
  • Pseudospectra & Matrix Pencils
  • Low Rank & Hierarchical Structures
  • Quadrature for Singular Integrals

Projects

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Integral Equations

Boundary Integral Equation in Acoustic Scattering fundamentals

Exploring the fundaments of Fredholm Alternative, Boundary Integrals Equation and Scattering Problems.

Research Interests

Computational Mathematics

PDE Solvers for Wave Scattering

Developing numerical solvers for partial differential equations describing wave propagation and scattering phenomena.

Optimization

Hierarchical Methods for Optimization

Designing hierarchical algorithms to accelerate the solution of large-scale optimization problems.

Approximation Theory

Rational Approximation

Constructing rational approximations for computational problems, including Zolotarev-type minimax approximation schemes.

Spectral Theory

Pseudospectra & Matrix Pencils

Developing computational methods and approximation theory for pseudospectra of matrix pencils.

Numerical Linear Algebra

Low Rank & Hierarchical Structures

Exploiting hierarchical and low-rank structure in transform matrices and dynamical systems for fast, scalable computation.

Numerical Analysis

Quadrature for Singular Integrals

Designing quadrature rules for accurately evaluating singular integrals arising in applied problems.