Zobrazeno 1 - 10
of 351
pro vyhledávání: '"65n99"'
Autor:
Helsing, Johan, Jiang, Shidong
A numerical scheme is presented for solving the Helmholtz equation with Dirichlet or Neumann boundary conditions on piecewise smooth open curves, where the curves may have corners and multiple junctions. Existing integral equation methods for smooth
Externí odkaz:
http://arxiv.org/abs/2411.05761
Configuration Optimization Problems (COPs), which involve minimizing a loss function over a set of discrete points $\boldsymbol{\gamma} \subset P$, are common in areas like Model Order Reduction, Active Learning, and Optimal Experimental Design. Whil
Externí odkaz:
http://arxiv.org/abs/2410.17938
In this work we address the problem of finding serendipity versions of approximate de Rham complexes with enhanced regularity. The starting point is a new abstract construction of general scope which, given three complexes linked by extension and red
Externí odkaz:
http://arxiv.org/abs/2407.12625
Autor:
Cubillos, Max, Jimenez, Edwin
This article presents novel numerical algorithms based on pseudodifferential operators for fast, direct, solution of the Helmholtz equation in 1D, 2D, and 3D inhomogeneous unbounded media. The proposed approach relies on an Operator Fourier Transform
Externí odkaz:
http://arxiv.org/abs/2407.09436
Neural operators such as the Fourier Neural Operator (FNO) have been shown to provide resolution-independent deep learning models that can learn mappings between function spaces. For example, an initial condition can be mapped to the solution of a pa
Externí odkaz:
http://arxiv.org/abs/2406.16740
This paper proposes localized subspace iteration (LSI) methods to construct generalized finite element basis functions for elliptic problems with multiscale coefficients. The key components of the proposed method consist of the localization of the or
Externí odkaz:
http://arxiv.org/abs/2406.09789
We present polynomial-augmented neural networks (PANNs), a novel machine learning architecture that combines deep neural networks (DNNs) with a polynomial approximant. PANNs combine the strengths of DNNs (flexibility and efficiency in higher-dimensio
Externí odkaz:
http://arxiv.org/abs/2406.02336
Beyond Linear Decomposition: a Nonlinear Eigenspace Decomposition for a Moist Atmosphere with Clouds
A linear decomposition of states underpins many classical systems. This is the case of the Helmholtz decomposition, used to split vector fields into divergence-free and potential components, and of the dry Boussinesq system in atmospheric dynamics, w
Externí odkaz:
http://arxiv.org/abs/2405.11107
The discretization of the deep Ritz method [18] for the Poisson equation leads to a high-dimensional non-convex minimization problem, that is difficult and expensive to solve numerically. In this paper, we consider the shallow Ritz approximation to o
Externí odkaz:
http://arxiv.org/abs/2404.17750
Autor:
Myrbäck, Sebastian, Zahedi, Sara
A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307 (2016)] i
Externí odkaz:
http://arxiv.org/abs/2404.10756