Schwarz
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Related Articles from SNS
Four-Level Overlapping Schwarz as Multigrid Coarse Solver for Incompressible Non-Newtonian Flow in Complex Geometries
arXiv:2606.01433v1 Announce Type: new Abstract: For complex geometries, the coarse problem of geometric multigrid can be too large to be solved by a direct solver. Here, we report on the use of domain decomposition applied to the multigrid coarse problem. Additive overlapping Schwarz methods are domain decomposition methods for the iterative solution of partial differential equations whose numerical and parallel scalability can be improved by the addition of coarse levels.
Uniform Schwarz Preconditioners for Variable-Degree $hp$ Finite Element Interface Problems
arXiv:2606.03141v1 Announce Type: new Abstract: We construct $h$- and $p$-robust, degree-preserving space decompositions and additive Schwarz preconditioners for variable-degree $hp$ finite element discretizations of reaction-diffusion and fitted-interface problems. On conforming simplicial meshes in arbitrary dimension, the single-domain result allows an arbitrary elementwise degree distribution subject only to $p_K\ge1$. A minimal-average Falk--Winther bubble transform is introduced by...
A Non-Overlapping Schwarz Hybrid Finite Element-Neural Operator Framework for Solid Mechanics on Irregular Domains
arXiv:2606.08796v1 Announce Type: new Abstract: Finite element (FE) methods are the benchmark for solid mechanics simulations, yet their computational cost becomes prohibitive for problems with localised nonlinearities, fine-scale features, or long-time dynamic evolution. In our earlier FE-neural operator (FE-NO) hybrid framework [1], physics-informed deep operator networks were coupled with FE solvers through overlapping domain decomposition with Dirichlet-Dirichlet interface exchange,...
Robust spectral preconditioning for high-P\'{e}clet number convection-diffusion
arXiv:2509.17531v2 Announce Type: replace Abstract: 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 element method (MS-GFEM), wherein the coarse space is spanned by locally optimal basis functions obtained from local generalized eigenproblems on operator-harmonic spaces. Extending the theory of Ma...
Quaternion Dirac--Coulomb--Breit Integral Transformation for Relativistic Four-Component Correlated Electronic Structure Theory
Announce Type: new Abstract: High-accuracy correlated four-component relativistic electronic structure methods are typically formulated in terms of integrals over molecular orbital (MO). Consequently, an efficient and scalable strategy is required to deal with the complexity of transforming relativistic two-electron integrals from the atomic orbital (AO) to the MO basis. The transformation bottleneck is particularly acute for approaches that include Breit interaction integrals, whose...
Nvidia Cosmos 3
Physical AI systems must understand the real world before they can act within it. Robots, autonomous vehicles, and smart spaces need to understand what’s happening in their world, predict what’s likely to happen next, and generate actions for specific environments, embodiments, and tasks. NVIDIA Cosmos 3 is a frontier foundation model for physical AI that combines physical reasoning, world generation, and action generation within a single open model.
Airbus-led consortium to launch German-backed fighter jet project after FCAS collapse
An Airbus-led alliance of eight defence firms will launch Team Gen 6 in Berlin, a German-backed sixth-generation fighter jet project intended to replace the collapsed Franco-German-Spanish FCAS programme, AFP reports. A new German-led fighter jet initiative is taking shape following the collapse of Europe's Future Combat Air System (FCAS) programme. An eight-company consortium dubbed 'Team Gen 6' and led by Airbus will be launched on Thursday in Berlin, the aerospace giant told AFP.
Parallel multilevel methods for solving the Darcy--Forchheimer model based on a nearly semicoercive formulation
Announce Type: replace Abstract: High-velocity fluid flow through porous media is modeled by prescribing a nonlinear relationship between the flow rate and the pressure gradient, called the Darcy--Forchheimer equation. This paper is concerned with the analysis of parallel multilevel methods for solving the Darcy--Forchheimer model. We begin by reformulating the Darcy--Forchheimer model as a nearly semicoercive convex optimization problem via the augmented Lagrangian method.
Airbus-led group proposes fighter jet alternative after French-German project fails
The FCAS programme had been viewed as a flagship European defence project, aimed at strengthening military cooperation as Europe faces a more assertive Russia. A consortium led by Airbus has proposed developing a next-generation fighter jet after the collapse of a high-profile Franco-German warplane programme, one of the companies involved told the AFP news agency on Tuesday. The move comes a day after German Chancellor Friedrich Merz and French President Emmanuel Macron ended the original...