Related papers: A parallel algorithm for unilateral contact proble…
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This paper proposes a combination of a hybrid CPU--GPU and a pure GPU software implementation of a direct algorithm for solving shifted linear systems $(A - \sigma I)X = B$ with large number of complex shifts $\sigma$ and multiple…
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Simulation of contact and friction dynamics is an important basis for control- and learning-based algorithms. However, the numerical difficulties of contact interactions pose a challenge for robust and efficient simulators. A…
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Non-overlapping domain decomposition methods are natural for solving interface problems arising from various disciplines, however, the numerical simulation requires technical analysis and is often available only with the use of high-quality…
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Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds. We present an algorithm for…
This paper presents a fast first-order method for solving the quasi-static contact problem with the Coulomb friction. It is known that this problem can be formulated as a second-order cone linear complementarity problem, for which…
Interface problems depict many fundamental physical phenomena and widely apply in the engineering. However, it is challenging to develop efficient fully decoupled numerical methods for solving degenerate interface problems in which the…
We consider a standard elliptic partial differential equation and propose a geometric multigrid algorithm based on Dirichlet-to-Neumann (DtN) maps for hybridized high-order finite element methods. The proposed unified approach is applicable…
In this paper, we aim to solve the system of equations governing linear elasticity in parallel using domain decomposition. Through a non-overlapping decomposition of the domain, our approach aims to target the resulting interface problem,…
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The last decade has witnessed an explosion in the development of models, theory and computational algorithms for "big data" analysis. In particular, distributed computing has served as a natural and dominating paradigm for statistical…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
In this paper, we study, from both variational and numerical points of view, a dynamic contact problem between a viscoelastic-viscoplastic piezoelectric body and a deformable obstacle. The contact is modelled using the classical normal…
A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant…