Computational Tools for PDEs with Complicated Geometries and Interfaces

Date & Time


Ingrid Daubechies Auditorium (IDA)

Integral equation methods offer a powerful unified framework for accurate modeling in fields such as acoustics, electromagnetics, elastostatics, nano-optics, microfluidics, biophysics, and geophysics, governed by PDEs such as the Laplace, Stokes, Helmholtz, Maxwell, Navier, heat and Navier-Stokes equations. For constant-coefficient problems, they reduce the unknowns to functions defined on the boundary alone. Even for variable-coefficient and nonlinear problems, they have distinct advantages over standard finite difference and finite element methods. Aiming at graduate students, postdocs, and practitioners, we will introduce the basic mathematical foundation of such methods, illustrate their use in applications, and offer expert-run hands-on tutorials using a set of efficient software tools. These tools allow large problems to be solved with high-order accuracy in a time almost linear in the number of unknowns (so-called “fast algorithms”). The integral equation framework is geometrically flexible, allowing for input from a variety of CAD formats and the incorporation of corner and edge singularities in bounded, unbounded or periodic domains. Topics will include: integral equation formulations, discretization, fast solvers, PDEs on surfaces, volumetric representations for variable-coefficient PDEs, and applications to steady-state and time-dependent problems.

Conference themes

  • Acoustic and electromagnetic scattering in the frequency domain
  • Biophysical and geological modeling
  • Surface PDEs
  • Software tools for boundary value problems in two and three dimensions
  • Fast direct and iterative solvers
  • Hierarchical Poincare Steklov solvers
  • Quadrature for singular integrals

For more detailed information go here.

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