相关论文: Highly Scalable Two-level Monolithic Overlapping S…

We present a preconditioning method for the linear systems arising from the boundary element discretization of the Laplace hypersingular equation on a $2$-dimensional triangulated surface $\Gamma$ in $\mathbb{R}^3$. We allow $\Gamma$ to…

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…

Efficient frequency-domain Full Waveform Inversion (FWI) of long-offset node data can be designed with a few discrete frequencies hence allowing for compact volume of data to be managed. Moreover, attenuation effects can be…

For non-preconditioned Galerkin systems, the condition number grows with the number of elements as well as the quotient of the maximal and the minimal mesh-size. Therefore, reliable and effective numerical computations, in particular on…

Elastic metasurfaces offer precise control over elastic waves for applications such as vibration isolation, sensing, and imaging. However, achieving high-efficiency and scattering-free performance with complex functionalities remains a…

For linear problems, domain decomposition methods can be used directly as iterative solvers, but also as preconditioners for Krylov methods. In practice, Krylov acceleration is almost always used, since the Krylov method finds a much better…

Invariant-based models for incompressible isotropic hyperelasticity are typically formulated as functions of the first and second invariants, $W = W(\bar{I}_1, \bar{I}_2)$. A widely used class of models employs separable representations of…

We discuss parallel (additive) and sequential (multiplicative) variants of overlapping Schwarz methods for the Helmholtz equation in $\mathbb{R}^d$, with large real wavenumber and smooth variable wave speed. The radiation condition is…

The increasing complexity and scale of photonic and electromagnetic devices demand efficient and accurate numerical solvers. In this work, we develop a parallel overlapping domain decomposition method (DDM) based on the finite-difference…

Domain decomposition methods (DDMs) provide a unifying framework for the scalable numerical solution of partial differential equations. Originating from Schwarz's alternating method, they have evolved into a rich family of algorithms that…

A symmetric and a nonsymmetric variant of the additive Schwarz preconditioner are proposed for the solution of a nonsymmetric system of algebraic equations arising from a general finite volume element discretization of symmetric elliptic…

Two-level domain decomposition preconditioners lead to fast convergence and scalability of iterative solvers. However, for highly heterogeneous problems, where the coefficient function is varying rapidly on several possibly non-separated…

The computation time for reservoir simulation is dominated by the linear solver. The sets of linear equations which arise in reservoir simulation have two distinctive features: the problems are usually highly anisotropic, with a dominant…

In this work, we consider the solution of fluid-structure interaction problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary…

In this work, we consider fracture propagation in nearly incompressible and (fully) incompressible materials using a phase-field formulation. We use a mixed form of the elasticity equation to overcome volume locking effects and develop a…

Solving large-scale Helmholtz problems discretized with high-order finite elements is notoriously difficult, especially in 3D where direct factorization of the system matrix is very expensive and memory demanding, and robust convergence of…

In this paper, we propose a two-level overlapping additive Schwarz domain decomposition preconditioner for the symmetric interior penalty discontinuous Galerkin method for the second order elliptic boundary value problem with highly…

The multigroup neutron transport criticality calculations using modern supercomputers have been widely employed in a nuclear reactor analysis for studying whether or not a system is self-sustaining. However, the design and development of…

We present and analyze a class of nonsymmetric preconditioners within a normal (weighted least-squares) matrix form for use in GMRES to solve nonsymmetric matrix problems that typically arise in finite element discretizations. An example of…

One of the state-of-the-art strategies for predicting crack propagation, nucleation, and interaction is the phase-field approach. Despite its reliability and robustness, the phase-field approach suffers from burdensome computational cost,…