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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
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