Applied Math Colloquium - Adrianna Gillman

Adrianna Gillman, Department of Applied Mathematics, University of Colorado Boulder

An efficient and high order accurate direct solution technique for variable coefficient elliptic partial differential equations

For many applications in science and engineering, the ability to efficiently and accurately approximate solutions to elliptic PDEs dictates what physical phenomena can be simulated numerically.  In this talk, we present a high-order accurate discretization technique for variable coefficient PDEs with smooth coefficients.  The technique comes with a nested dissection inspired direct solver that scales linearly or nearly linearly with respect to the number of unknowns. 

Unlike the application of nested dissection methods to classic discretization techniques, the constant prefactors do not grow with the order of the discretization.   The discretization is robust even for problems with highly oscillatory solutions.  For example, a problem 100 wavelengths in size can be solved to 9 digits of accuracy with 3.7 million unknowns on a desktop computer.  The precomputation of the direct solver takes 6 minutes on a desktop computer.  Then applying the computed solver takes 3 seconds.  A parallel implementation of the solution technique reduces the precomputation time to roughly 30 seconds and halves the time it takes to apply the solver.  Applications of the solution technique to inverse scattering problems and time dependent partial differential equations will also be presented.  

 

Friday, August 30, 2019 at 3:00pm to 4:00pm

Engineering Center, ECCR 245
1111 Engineering Drive, Boulder, CO 80309

Event Type

Colloquium/Seminar

Interests

Science & Technology, Research & Innovation

Audience

Students, Faculty, General Public, Postdoc

College, School & Unit

Engineering & Applied Science

Tags

colloquium

Group
Applied Mathematics
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