Related papers: Non-invasive multigrid for semi-structured grids
Multigrid is a powerful solver for large-scale linear systems arising from discretized partial differential equations. The convergence theory of multigrid methods for symmetric positive definite problems has been well developed over the…
The creation of a volumetric mesh representing the interior of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not…
Simulation of multiphase poromechanics involves solving a multi-physics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also…
Hypergraphs, which use hyperedges to capture groupwise interactions among different entities, have gained increasing attention recently for their versatility in effectively modeling real-world networks. In this paper, we study the problem…
Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…
This paper describes a massively parallel algebraic multigrid method based on non-smoothed aggregation. It is especially suited for solving heterogeneous elliptic problems as it uses a greedy heuristic algorithm for the aggregation that…
Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and…
Lattice metamaterials enable lightweight, multifunctional structures, yet homogenization-based evaluation of their effective properties remains computationally expensive. Neural surrogates offer speed but often lack the accuracy and…
In recent years, topology optimization has been developed sufficiently and many researchers have concentrated on enhancing to computationally numerical algorithms for computational effectiveness of this method. Along with the development of…
Hierarchical code coupling strategies make it possible to combine the results of individual numerical solvers into a self-consistent symplectic solution. We explore the possibility of allowing such a coupling strategy to be non-intrusive.…
The challenge to fully exploit the potential of existing and upcoming scientific instruments like large single-dish radio telescopes is to process the collected massive data effectively and efficiently. As a "quasi 2D stencil computation"…
Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD) linear systems resulting from the discretization of general elliptic PDEs, or the spatial discretization of parabolic PDEs. However, convergence…
Multigrid methods are asymptotically optimal algorithms ideal for large-scale simulations. But, they require making numerous algorithmic choices that significantly influence their efficiency. Unlike recent approaches that learn optimal…
The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…
We present a monolithic $hp$ space-time multigrid method for tensor-product space-time finite element discretizations of the Stokes equations. Geometric and polynomial coarsening of the space-time mesh is performed, and the entire algorithm…
We consider an efficient computational framework for speeding up several machine learning algorithms with almost no loss of accuracy. The proposed framework relies on projections via structured matrices that we call Structured Spinners,…
Multi-Party Computation in the Head (MPCitH) algorithms are appealing candidates in the additional US NIST standardization rounds for Post-Quantum Cryptography (PQC) with respect to key sizes and mathematical hardness assumptions. However,…
Despite the rapidly evolving field of computational electromagnetics, few open-source tools have managed to tackle the problem of automatic mesh generation for properly discretizing the problem of interest into a finite set of elements…
We develop a robust solver for a mixed finite element convex splitting scheme for the Cahn-Hilliard equation. The key ingredient of the solver is a preconditioned minimal residual algorithm (with a multigrid preconditioner) whose…
A few grid-computing tools are available for public use. However, such systems are usually quite complex and require several man-months to set up. In case the user wishes to set-up an ad-hoc grid in a small span of time, such tools cannot…