Related papers: A geometrically informed algebraic multigrid preco…
We propose an adaptive multigrid preconditioning technology for solving linear systems arising from Discontinuous Petrov-Galerkin (DPG) discretizations. Unlike standard multigrid techniques, this preconditioner involves only trace spaces…
In this paper, the authors constructed an auxiliary space multigrid preconditioner for the weak Galerkin finite element method for second-order diffusion equations, discretized on simplicial 2D or 3D meshes. The idea of the auxiliary space…
Physics-Informed Neural Networks (PINNs) have gained considerable interest in diverse engineering domains thanks to their capacity to integrate physical laws into deep learning models. Recently, geometry-aware PINN-based approaches that…
In the domain of geometry and topology optimization, discovering geometries that optimally satisfy specific problem criteria is a complex challenge in both engineering and scientific research. In this work, we propose a new approach for the…
We present families of space-time finite element methods (STFEMs) for a coupled hyperbolic-parabolic system of poro- or thermoelasticity. Well-posedness of the discrete problems is proved. Higher order approximations inheriting most of the…
Presented in this paper is a new sparse linear solver methodology motivated by multigrid principles and based around general local transformations that diagonalize a matrix while maintaining its sparsity. These transformations are…
The Shifted Boundary Method (SBM) trades some part of the burden of body-fitted meshing for increased algebraic complexity. While the resulting linear systems retain the standard $\mathcal{O}(h^{-2})$ conditioning of second-order operators,…
This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on…
As datasets used in scientific applications become more complex, studying the geometry and topology of data has become an increasingly prevalent part of the data analysis process. This can be seen for example with the growing interest in…
Artificial intelligence for scientific discovery has recently generated significant interest within the machine learning and scientific communities, particularly in the domains of chemistry, biology, and material discovery. For these…
Large-scale contact mechanics simulations are crucial in many engineering fields such as structural design and manufacturing. In the frictionless case, contact can be modeled by minimizing an energy functional; however, these problems are…
The prediction of molecular properties is a crucial task in the field of material and drug discovery. The potential benefits of using deep learning techniques are reflected in the wealth of recent literature. Still, these techniques are…
Current graph clustering methods emphasize individual node and edge con nections, while ignoring higher-order organization at the level of motif. Re cently, higher-order graph clustering approaches have been designed by motif based…
We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property…
In this work, we present a general framework for the design and analysis of two-level AMG methods. The approach is to find a basis for locally optimal or quasi-optimal coarse space, such as the space of constant vectors for standard…
Elliptic partial differential equations (PDEs) frequently arise in continuum descriptions of physical processes relevant to science and engineering. Multilevel preconditioners represent a family of scalable techniques for solving discrete…
We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…
Engineering design involves demanding models encompassing many decision variables and uncontrollable parameters. In addition, unavoidable aleatoric and epistemic uncertainties can be very impactful and add further complexity. The…
We propose an end-to-end pipeline to robustly generate high-quality, high-order and coarse quadrilateral meshes on CAD models. This kind of mesh enables the use of high-order analysis techniques such as high-order finite element methods or…
Preconditioning is at the heart of iterative solutions of large, sparse linear systems of equations in scientific disciplines. Several algebraic approaches, which access no information beyond the matrix itself, are widely studied and used,…