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In this work we design a new domain decomposition method for the Euler equations in 2 dimensions. The basis is the equivalence via the Smith factorization with a third order scalar equation to whom we can apply an algorithm inspired from…

Numerical Analysis · Mathematics 2009-09-04 Victorita Dolean , Frédéric Nataf

We introduce a two-level hybrid restricted additive Schwarz (RAS) preconditioner for heterogeneous steady-state convection-diffusion equations at high P\'{e}clet numbers. Our construction builds on the multiscale spectral generalized finite…

Numerical Analysis · Mathematics 2025-09-23 Lukas Holbach , Peter Bastian , Robert Scheichl

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…

Numerical Analysis · Mathematics 2025-09-26 Youngkyu Lee , Alena Kopaničáková , George Em Karniadakis

Splitting methods constitute a well-established class of numerical schemes for the time integration of partial differential equations. Their main advantages over more traditional schemes are computational efficiency and superior geometric…

Numerical Analysis · Mathematics 2017-01-06 Lukas Einkemmer , Alexander Ostermann

In this article, a two-level overlapping domain decomposition preconditioner is developed for solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media. Our preconditioner starts at a mixed finite element…

Numerical Analysis · Mathematics 2024-03-29 Changqing Ye , Shubin Fu , Eric T. Chung , Jizu Huang

We theoretically studied electric double layer by using the mean-field approach including the non-uniform size effect and the orientational ordering of water dipoles in electrolyte solution. Performing the minimization of the free energy,…

Soft Condensed Matter · Physics 2022-02-15 Jun-Sik Sin , Kwang-Il Kim , Chung-Sik Sin

In the Super-Transition-Array statistical method for the computation of radiative opacity of hot dense matter, the moments of the absorption or emission features involve partition functions with reduced degeneracies, occurring through the…

Atomic Physics · Physics 2024-05-14 Jean-Christophe Pain , Brian Wilson

The partition problem is a well-known basic NP-complete problem. We mainly consider the optimization version of it in this paper. The problem has been investigated from various perspectives for a long time and can be solved efficiently in…

Discrete Mathematics · Computer Science 2024-05-10 Susumu Kubo

Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel…

Numerical Analysis · Mathematics 2013-11-19 Eugene Vecharynski , Yousef Saad , Masha Sosonkina

In this paper, we analyze the spectra of the preconditioned matrices arising from discretized multi-dimensional Riesz spatial fractional diffusion equations. The finite difference method is employed to approximate the multi-dimensional…

Numerical Analysis · Mathematics 2022-06-07 Xin Huang , Xue-Lei Lin , Michael K. Ng , Hai-Wei Sun

Recently, $4$-regular partitions into distinct parts are connected with a family of overpartitions. In this paper, we provide a uniform extension of two relations due to Andrews for the two types of partitions. Such an extension is made…

Combinatorics · Mathematics 2023-01-27 George E. Andrews , Shane Chern

Discrete element method simulations of confined bidisperse granular shear flows elucidate the balance between diffusion and segregation that can lead to either mixed or segregated states, depending on confining pressure. Results indicate…

Soft Condensed Matter · Physics 2018-09-24 Alexander M. Fry , Paul B. Umbanhowar , Julio M. Ottino , Richard M. Lueptow

We propose a novel universal construction of two-level overlapping Schwarz preconditioners for $2m$th-order elliptic boundary value problems, where $m$ is a positive integer. The word "universal" here signifies that the coarse space…

Numerical Analysis · Mathematics 2025-11-11 Jongho Park

We study the convergence properties of an overlapping Schwarz decomposition algorithm for solving nonlinear optimal control problems (OCPs). The algorithm decomposes the time domain into a set of overlapping subdomains, and solves all…

Optimization and Control · Mathematics 2026-05-11 Sen Na , Sungho Shin , Mihai Anitescu , Victor M. Zavala

For diffusion-reaction equations employing a splitting procedure is attractive as it reduces the computational demand and facilitates a parallel implementation. Moreover, it opens up the possibility to construct second-order integrators…

Numerical Analysis · Mathematics 2017-01-06 Lukas Einkemmer , Alexander Ostermann

In this paper we are concerned with restricted additive Schwarz with local impedance transformation conditions for a family of Helmholtz problems in two dimensions. These problems are discretized by the finite element method with conforming…

Numerical Analysis · Mathematics 2024-02-13 Qiya Hu , Ziyi Li

The convergence rate of domain decomposition methods (DDMs) strongly depends on the transmission condition at the interfaces between subdomains. Thus, an important aspect in improving the efficiency of such solvers is careful design of…

Numerical Analysis · Mathematics 2025-05-19 Niall Bootland , Sahar Borzooei , Victorita Dolean , Pierre-Henri Tournier

We consider a microscopic model of spacetime, where spacetime is assumed to be a specific graph with Planck size quantum black holes on its vertices. As a thermodynamical system under consideration we take a certain uniformly accelerating,…

General Relativity and Quantum Cosmology · Physics 2008-10-28 Jarmo Makela

In this article, we first investigate the partitions whose parts are congruent to $a$ or $b$ modulo $k$ with the aid of separable integer partition classes with modulus $k$ introduced by Andrews. Then, we introduce the…

Combinatorics · Mathematics 2024-07-01 Thomas Y. He , C. S. Huang , H. X. Li , X. Zhang

In this note, we study the determinantal structure of the $k$-th conditional expectation of the overlap for induced spherical unitary ensemble. We will show the universality for the scaling limits of the $k$-the conditional expectation of…

Mathematical Physics · Physics 2024-08-23 Kohei Noda