Transmission operators for the non-overlapping Schwarz method for solving Helmholtz problems in rectangular cavities

05/13/2022
by   Nicolas Marsic, et al.
0

In this paper we discuss different transmission operators for the non-overlapping Schwarz method which are suited for solving the time-harmonic Helmholtz equation in cavities (i.e. closed domains which do not feature an outgoing wave condition). Such problems are heavily impacted by back-propagating waves which are often neglected when devising optimized transmission operators for the Schwarz method. This work explores new operators taking into account those back-propagating waves and compares them with well-established operators neglecting these contributions. Notably, this paper focuses on the case of rectangular cavities, as the optimal (non-local) transmission operator can be easily determined. Nonetheless, deviations from this ideal geometry are considered as well. In particular, computations of the acoustic noise in a three-dimensional model of the helium vessel of a beamline cryostat with optimized Schwarz schemes are discussed. Those computations show a reduction of 46 for cavities with those optimized for unbounded problems.

READ FULL TEXT
research
01/06/2020

Convergence of optimized non-overlapping Schwarz method for Helmholtz problems in closed domains

In this paper we discuss the convergence of state-of-the-art optimized S...
research
10/05/2022

On the non-local boundary value problem from the probabilistic viewpoint

We provide a short introduction of new and well-known facts relating non...
research
08/08/2021

Non-self adjoint impedance in Generalized Optimized Schwarz Methods

We present a convergence theory for Optimized Schwarz Methods that rely ...
research
03/14/2020

Robust treatment of cross points in Optimized Schwarz Methods

In the field of Domain Decomposition (DD), Optimized Schwarz Method (OSM...
research
11/28/2019

Optimized Runge-Kutta (LDDRK) timestepping schemes for non-constant-amplitude oscillations

Finite differences and Runge-Kutta time stepping schemes used in Computa...
research
04/20/2022

Closed form optimized transmission conditions for complex diffusion with many subdomains

Optimized transmission conditions in domain decomposition methods have b...
research
12/20/2022

On exact truncation of backward waves in elastrodynamics

For elastic wave scattering problems in unbounded anisotropic media, the...

Please sign up or login with your details

Forgot password? Click here to reset