Grainger College of Engineering Seminars & Speakers

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COLLOQUIUM: Adrianna Gillman, "Accurate and Efficient Solution Techniques for Helmholtz Problems in Variable Medium"

Event Type
Seminar/Symposium
Sponsor
Siebel School of Computing and Data Science
Location
HYBRID: 2405 Siebel Center for Computer Science or online
Virtual
wifi event
Date
Nov 11, 2024   3:30 pm  
Views
131
Originating Calendar
Siebel School Colloquium Series

Zoom: https://illinois.zoom.us/j/86436404596?pwd=vd3U7RPsbwIdSzVdhgBsaUzcASb3H9.1

Refreshments Provided.

Abstract: 
The ability to robustly and efficiently solve Helmholtz problems has been plagued by the 
so-called pollution effect and the introduction of artificial resonances by discretization. We will present the Hierarchical Poincare-Steklov (HPS) method which does not observe these shortcomings. This new solution technique is often viewed as combining a composite spectral method with an efficient solver. The uniqueness of the discretization lies in the coupling of elements via Poincare-Steklov operators such as the Dirichlet-to-Neumann operator. This presentation will demonstrate that the HPS method effectively and easily solves two-dimensional high-frequency Helmholtz problems. We will share the progress made toward making the HPS method a computationally feasible solution technique for three-dimensional problems. For example, a three-dimensional problem approximately 100 wavelengths in size can be solved to 4 digits of accuracy in 17 minutes with over 1 billion discretization points. Additionally, a problem 50 wavelengths in size can be solved to 8 digits of accuracy in 26 minutes with the same number of discretization points.

Bio:
The ability to robustly and efficiently solve Helmholtz problems has been plagued by the so-called pollution effect and the introduction of artificial resonances by discretization. We will present the Hierarchical Poincare-Steklov (HPS) method which does not observe these shortcomings. This new solution technique is often viewed as combining a composite spectral method with an efficient solver. The uniqueness of the discretization lies in the coupling of elements via Poincare-Steklov operators such as the Dirichlet-to-Neumann operator. This presentation will demonstrate that the HPS method effectively and easily solves two-dimensional high-frequency Helmholtz problems. We will share the progress made toward making the HPS method a computationally feasible solution technique for three-dimensional problems. For example, a three-dimensional problem approximately 100 wavelengths in size can be solved to 4 digits of accuracy in 17 minutes with over 1 billion discretization points. Additionally, a problem 50 wavelengths in size can be solved to 8 digits of accuracy in 26 minutes with the same number of discretization points.


Part of the Siebel School Speakers Series. Faculty Host: Andreas Kloeckner 


Meeting ID: 864 3640 4596 
Passcode: csillinois


If accommodation is required, please email <erink@illinois.edu> or <communications@cs.illinois.edu>. Someone from our staff will contact you to discuss your specific needs



 

 

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