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pro vyhledávání: '"65m55"'
Parallel-in-time (PinT) techniques have been proposed to solve systems of time-dependent differential equations by parallelizing the temporal domain. Among them, Parareal computes the solution sequentially using an inaccurate (fast) solver, and then
Externí odkaz:
http://arxiv.org/abs/2411.06225
Autor:
Müller, Eike Hermann
The incompressible Euler equations are an important model system in computational fluid dynamics. Fast high-order methods for the solution of this time-dependent system of partial differential equations are of particular interest: due to their expone
Externí odkaz:
http://arxiv.org/abs/2410.09790
The paper considers an inverse problem of reconstructing the spatially distributed complex dielectric permittivity function using backscattered data of the electric field in the frequency domain. We develop iterative algorithm for reconstruction of t
Externí odkaz:
http://arxiv.org/abs/2410.20689
We enhance machine learning algorithms for learning model parameters in complex systems represented by ordinary differential equations (ODEs) with domain decomposition methods. The study evaluates the performance of two approaches, namely (vanilla) P
Externí odkaz:
http://arxiv.org/abs/2410.01599
Autor:
Lei, Wei-Min, Li, Hou-Biao
Neural operators are effective tools for solving parametric partial differential equations (PDEs). They can predict solutions of PDEs with different initial and boundary conditions, as well as different input functions. The recently proposed Wavelet
Externí odkaz:
http://arxiv.org/abs/2408.08190
Autor:
Engström, Emil, Hansen, Eskil
Recently, their has been development of an abstract approach to the Robin--Robin method, enabling the treatment of linear and nonlinear elliptic and parabolic equations on Lipschitz domains within one framework. However, previously this setting has n
Externí odkaz:
http://arxiv.org/abs/2408.07392
Autor:
Margenberg, Nils, Munch, Peter
We present a space-time multigrid method based on tensor-product space-time finite element discretizations. The method is facilitated by the matrix-free capabilities of the {\ttfamily deal.II} library. It addresses both high-order continuous and disc
Externí odkaz:
http://arxiv.org/abs/2408.04372
Autor:
Jackaman, James, MacLachlan, Scott
Space-time finite-element discretizations are well-developed in many areas of science and engineering, but much work remains within the development of specialized solvers for the resulting linear and nonlinear systems. In this work, we consider the a
Externí odkaz:
http://arxiv.org/abs/2407.13997
MgFNO: Multi-grid Architecture Fourier Neural Operator for Parametric Partial Differential Equations
Autor:
Guo, Zi-Hao, Li, Hou-Biao
In science and engineering, there is often a need to repeatedly solve large-scale and high-resolution partial differential equations (PDEs). Neural operators are a new model that can map between function spaces, allowing trained models to emulate PDE
Externí odkaz:
http://arxiv.org/abs/2407.08615
We introduce a novel two-level overlapping additive Schwarz preconditioner for accelerating the training of scientific machine learning applications. The design of the proposed preconditioner is motivated by the nonlinear two-level overlapping additi
Externí odkaz:
http://arxiv.org/abs/2406.10997