Grote, Marcus J. and Nataf, Frédéric and Tang, Jet Hoe and Tournier, PierreHenri. (2019) Scalable Parallel Methods for the Helmholtz Equation via Exact Controllability. In: 14th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2019). Wien.
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Official URL: https://edoc.unibas.ch/75312/
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Abstract
Largescale Helmholtz problems are notoriously difficult to solve with standard iterative methods, in fact increasingly so, the higher the frequency ω > 0. Controllability methods (CM) offer an alternative approach for the numerical solution of the Helmholtz equation. Instead of solving the problem directly in the frequency domain, we first transform it back to the time domain where we seek the timeperiodic solution y(.,t) of the corresponding timedependent wave equation with known period T = (2π)/ω. By minimizing a cost functional, which penalizes the mismatch after one period, CM iteratively steer y towards the desired periodic state. Here, we consider two different approaches based either on the first or secondorder formulation of the wave equation. Both are extended to general boundaryvalue problems governed by the Helmholtz equation and lead to robust and inherently parallel algorithms. Numerical results illustrate the accuracy and strong scalability of CM with up to a billion unknowns on massively parallel architectures.
Faculties and Departments:  05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Numerik (Grote) 

UniBasel Contributors:  Grote, Marcus J. 
Item Type:  Conference or Workshop Item, refereed 
Conference or workshop item Subtype:  Conference Paper 
Publisher:  TU Wien 
ISBN:  9783200065116 
Note:  Publication type according to Uni Basel Research Database: Conference paper 
Identification Number: 

Last Modified:  10 Mar 2020 09:17 
Deposited On:  10 Mar 2020 09:17 
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