Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution
Most modeling approaches lie in either of the two categories: physics‐based or data‐driven.
Recently, a third approach which is a combination of these deterministic and statistical …
Recently, a third approach which is a combination of these deterministic and statistical …
Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation
We analyse parallel overlapping Schwarz domain decomposition methods for the Helmholtz
equation, where the exchange of information between subdomains is achieved using first …
equation, where the exchange of information between subdomains is achieved using first …
High-order, dispersionless “fast-hybrid” wave equation solver. Part I: O (1) sampling cost via incident-field windowing and recentering
TG Anderson, OP Bruno, M Lyon - SIAM Journal on Scientific Computing, 2020 - SIAM
This paper proposes a frequency/time hybrid integral-equation method for the time-
dependent wave equation in two-and three-dimensional spatial domains. Relying on Fourier …
dependent wave equation in two-and three-dimensional spatial domains. Relying on Fourier …
[HTML][HTML] An explicit substructuring method for overlapping domain decomposition based on stochastic calculus
Abstract In a recent paper [7], a hybrid supercomputing algorithm for elliptic equations has
been proposed. The idea is that the interfacial nodal solutions solve a linear system, whose …
been proposed. The idea is that the interfacial nodal solutions solve a linear system, whose …
Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition
D Lafontaine, EA Spence - Pure and Applied Analysis, 2023 - msp.org
We prove sharp bounds on certain impedance-to-impedance maps (and their compositions)
for the Helmholtz equation with large wavenumber (ie, at high frequency) using …
for the Helmholtz equation with large wavenumber (ie, at high frequency) using …
Quantitative bounds on Impedance-to-Impedance operators with applications to fast direct solvers for PDEs
T Beck, Y Canzani, JL Marzuola - Pure and Applied Analysis, 2022 - msp.org
We prove quantitative norm bounds for a family of operators involving impedance boundary
conditions on convex, polygonal domains. A robust numerical construction of Helmholtz …
conditions on convex, polygonal domains. A robust numerical construction of Helmholtz …
Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies
We develop a non-overlapping domain decomposition method (DDM) for scalar wave
scattering by periodic layered media. Our approach relies on robust boundary-integral …
scattering by periodic layered media. Our approach relies on robust boundary-integral …
Multitrace/singletrace formulations and domain decomposition methods for the solution of Helmholtz transmission problems for bounded composite scatterers
We present Nyström discretizations of multitrace/singletrace formulations and non-
overlapping Domain Decomposition Methods (DDM) for the solution of Helmholtz …
overlapping Domain Decomposition Methods (DDM) for the solution of Helmholtz …
Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition
D Lafontaine, EA Spence - arXiv preprint arXiv:2211.14659, 2022 - arxiv.org
We prove sharp bounds on certain impedance-to-impedance maps (and their compositions)
for the Helmholtz equation with large wavenumber (ie, at high-frequency) using …
for the Helmholtz equation with large wavenumber (ie, at high-frequency) using …
Fast factorization update for general elliptic equations under multiple coefficient updates
For discretized elliptic equations, we develop a new factorization update algorithm that is
suitable for incorporating coefficient updates with large support and large magnitude in …
suitable for incorporating coefficient updates with large support and large magnitude in …