相关论文: A p-multigrid method enhanced with an ILUT smoothe…

Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…

When used to accelerate the convergence of fixed-point iterative methods, such as the Picard method, which is a kind of nonlinear fixed-point iteration, polynomial extrapolation techniques can be very effective. The numerical solution of…

Isogeometric cohesive elements are presented for modeling two and three dimensional delaminated composite structures. We exploit the knot insertion algorithm offered by NURBS (Non Uniform Rational B-splines) to generate cohesive elements…

Isogeometric Analysis (IgA) is a spline based approach to the numerical solution of partial differential equations. There are two major issues that IgA was designed to address. The first issue is the exact representation of domains stemming…

The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one…

Isogeometrically enriched finite elements offer efficient localized isogeometric analysis (IGA) enrichment for numerical simulations involving large computational domains. This is achieved by employing surface enriched elements to interface…

Domain-specific hardware to solve computationally hard optimization problems has generated tremendous excitement. Here, we evaluate probabilistic bit (p-bit) based Ising Machines (IM) on the 3-regular 3-Exclusive OR Satisfiability (3R3X),…

With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs, high-performance computing applications can benefit from lower precision at appropriate spots to speed up the overall execution time. In this paper, we investigate…

We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…

Multigrid methods are popular iterative methods for solving large-scale sparse systems of linear equations. We present a mixed precision formulation of the multigrid V-cycle with general assumptions on the finite precision errors coming…

This paper compares the performance of seven different element agglomeration algorithms on unstructured triangular/tetrahedral meshes when used as part of a geometric multigrid. Five of these algorithms come from the literature on AMGe…

This work develops user-friendly a posteriori error estimates of finite element methods, based on smoothers of linear iterative solvers. The proposed method employs simple smoothers, such as Jacobi or Gauss-Seidel iteration, on an auxiliary…

Multi-material problems often exhibit complex geometries along with physical responses presenting large spatial gradients or discontinuities. In these cases, providing high-quality body-fitted finite element analysis meshes and obtaining…

In this study, we propose the lopsided HSS (LHSS) iteration method for solving a class of complex symmetric indefinite systems of linear equations. This method employs an alternating iterative scheme, where each iteration entails solving…

FFT-based solvers introduced in the 1990s for the numerical homogenization of heterogeneous elastic materials have been extended to a wide range of physical properties. In parallel, alternative algorithms and modified discrete Green…

We propose the first optimal geometric multigrid solver for hybrid high-order discretizations that can handle arbitrary polytopal agglomeration hierarchies in both two and three dimensions. The key ingredient is the use of modified skeleton…

In recent publications, the author and his coworkers have proposed a multigrid method for solving linear systems arizing from the discretization of partial differential equations in isogeometric analysis and have proven that the convergence…

We present a novel method for solving high-order partial differential equations (PDEs) over planar multi-patch geometries demonstrated on the basis of the polyharmonic equation of order $m$, $m \geq 1$, which is a particular linear elliptic…

We present an adaptive scheme for isogeometric phase-field modeling, to perform suitably graded hierarchical refinement and coarsening on both single- and multi-patch geometries by considering truncated hierarchical spline constructions…

In the present work, we study how to develop an efficient solver for the fast resolution of large and sparse linear systems that occur while discretizing elliptic partial differential equations using isogeometric analysis. Our new approach…