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Low-rank solutions to the stochastic Helmholtz equation

Autoren: A. Kaya, M.A. Freitag (2024)

In this paper, we consider low-rank approximations for the solutions to the stochastic Helmholtz equation with random coefficients. A Stochastic Galerkin finite element method is used for the discretization of the Helmholtz problem. Existence theory for the low-rank approximation is established when the system matrix is indefinite. The low-rank algorithm does not require the construction of a large system matrix which results in an advantage in terms of CPU time and storage. Numerical results show that, when the operations in a low-rank method are performed efficiently, it is possible to obtain an advantage in terms of storage and CPU time compared to computations in full rank. We also propose a general approach to implement a preconditioner using the low-rank format efficiently.

Zeitschrift:
Journal of Computational and Applied Mathematics
Seiten:
In Press

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Anschrift

Universität Potsdam
Institut für Mathematik
Campus Golm, Haus 9
Karl-Liebknecht-Str. 24-25
D-14476 Potsdam

Aktivitäten

15.11.2024, 10:00  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis

From modular graph forms to iterated integrals (Part 2)

Emil Claasen (MPI, Potsdam)

Abstract: Modular Graph Forms (MGFs) are a class of modular forms represented by lattice sums associated to directed simple graphs. They originated from the calculation of graviton amplitudes in type... 

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15.11.2024, 11:00  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis

Renormalising Non-Commutative Singular PDEs

Martin Peev (Inperial College, London) (online)

When attempting to construct QFTs that include Fermions using the methods of Stochastic Quantisation, one is naturally forced to consider noncommutative stochastic PDEs. I shall show how to formulate... 

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20.11.2024, 14:00 - 16:00 (Special session)  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Institutskolloquium

Quantitative elliptic homogenization: at the interface of PDEs, probability theory and statistical physics

Mitia Duerinckx (Brussel), Marius Lemm (Tübingen)

14:00  Mitia Duerinckx (Bruxelles):  Quantitative elliptic homogenization: a regularity perspective and Bourgain's surprising insight.
14:45  Tea and Coffee Break
15:15  Marius Lemm (Tübingen): ... 

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22.11.2024, 11:00  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis

Matched pairs, post-Hopf algebras and the quantum Yang-Baxter equation

Yunan Li (Guangzhong, China) (online)

Recently, Ferri and Sciandra introduced two equivalent notions, matched pair of actions on a Hopf algebra and Yetter-Drinfeld brace. Any of these objects actually provides a solution of the quantum... 

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27.11. bis 29.11.2024  –  Campus "Am Neuen Palais" Building 8, Seminar room 0.58
Konferenz

QFT Workshop

Analytical methods in interplay with physics

A workshop to explore Asymptotics, Randomness and Noncommutativity

This three day workshop aims at fostering interactions between mathematicians who use... 

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