Related papers: A Parallel Scalable Domain Decomposition Precondit…
In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, our goal is a contribution towards the development of…
CFD users of supercomputers usually resort to rule-of-thumb methods to select the number of subdomains (partitions) when relying on MPI-based parallelization. One common approach is to set a minimum number of elements or cells per…
We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…
In this paper we propose a variant of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the proposed preconditioner, we use the simplest coarse solver…
A hydraulic fracturing system with super-hydrophobic proppants is characterized by a transient triple-porosity Navier-Stokes model. For this complex multiphysics system, particularly in the context of three-dimensional space, a local…
In this paper we present an algebraic dimension-oblivious two-level domain decomposition solver for discretizations of elliptic partial differential equations. The proposed parallel solver is based on a space-filling curve partitioning…
In this paper, we propose and analyze an additive domain decomposition method (DDM) for solving the high-frequency Helmholtz equation with the Sommerfeld radiation condition. In the proposed method, the computational domain is partitioned…
This paper applies topology optimisation to the design of structures with periodic microstructural details without length scale separation, i.e. considering the complete macroscopic structure and its response, while resolving all…
An iteration-free method of domain decomposition is considered for approximate solving a boundary value problem for a second-order parabolic equation. A standard approach to constructing domain decomposition schemes is based on a partition…
Our research focuses on the development of domain decomposition preconditioners tailored for second-order elliptic partial differential equations. Our approach addresses two major challenges simultaneously: i) effectively handling…
Solving the normal equations corresponding to large sparse linear least-squares problems is an important and challenging problem. For very large problems, an iterative solver is needed and, in general, a preconditioner is required to…
In this work, we propose two-level space-time domain decomposition preconditioners for parabolic problems discretized using finite elements. They are motivated as an extension to space-time of balancing domain decomposition by constraints…
Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…
We propose an algorithm for the efficient parallel implementation of elastoplastic problems with hardening based on the so-called TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. We consider an…
Modern supercomputers allow the simulation of complex phenomena with increased accuracy. Eventually, this requires finer geometric discretizations with larger numbers of mesh elements. In this context, and extrapolating to the Exascale…
This paper studies the nucleus decomposition problem, which has been shown to be useful in finding dense substructures in graphs. We present a novel parallel algorithm that is efficient both in theory and in practice. Our algorithm achieves…
Many scientific and engineering challenges can be formulated as optimization problems which are constrained by partial differential equations (PDEs). These include inverse problems, control problems, and design problems. As a major…
Purpose: To introduce a novel deep learning based approach for fast and high-quality dynamic multi-coil MR reconstruction by learning a complementary time-frequency domain network that exploits spatio-temporal correlations simultaneously…
As the number of processor cores on supercomputers becomes larger and larger, algorithms with high degree of parallelism attract more attention. In this work, we propose a novel space-time coupled algorithm for solving an inverse problem…
The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of…