Related papers: Efficient distributed matrix-free multigrid method…
High-order partial differential equations (PDEs) require derivative regularity that standard $C^0$ finite element infrastructures do not directly provide on unstructured meshes. We propose a mesh-intrinsic generalized finite element method…
In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems. We discuss the challenges associated with mechanics and flow problems in…
In many numerical schemes, the computational complexity scales non-linearly with the problem size. Solving a linear system of equations using direct methods or most iterative methods is a typical example. Algebraic multi-grid (AMG) methods…
Typical areas of application of explicit dynamics are impact, crash test, and most importantly, wave propagation simulations. Due to the numerically highly demanding nature of these problems, efficient automatic mesh generators and…
The dual continuum model serves as a powerful tool in the modeling of subsurface applications. It allows a systematic coupling of various components of the solutions. The system is of multiscale nature as it involves high heterogeneous and…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…
Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (FMM) appears as a rising star. Our previous recent work showed scaling of an FMM on GPU clusters, with problem sizes in the…
General Matrix Multiplication (GEMM) is a crucial algorithm for various applications such as machine learning and scientific computing, and an efficient GEMM implementation is essential for the performance of these systems. While…
Skin modeling is an ongoing research area that highly benefits from modern parallel algorithms. This article aims at applying shape optimization to compute cell size and arrangement for elastic energy minimization of a cellular composite…
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…
Discontinuous Galerkin (dG) methods on meshes consisting of polygonal/polyhedral (henceforth, collectively termed as \emph{polytopic}) elements have received considerable attention in recent years. Due to the physical frame basis functions…
In this paper, we propose an efficient parallelization strategy for boundary element method (BEM) solvers that perform the electromagnetic analysis of structures with lossy conductors. The proposed solver is accelerated with the adaptive…
Complex mechanic systems simulation is important in many real-world applications. The de-facto numeric solver using Finite Element Method (FEM) suffers from computationally intensive overhead. Though with many progress on the reduction of…
We present an easy to use and flexible grid library for developing highly scalable parallel simulations. The distributed cartesian cell-refinable grid (dccrg) supports adaptive mesh refinement and allows an arbitrary C++ class to be used as…
Parallel finite element algorithms based on object-oriented concepts are presented. Moreover, the design and implementation of a data structure proposed are utilized in realizing a parallel geometric multigrid method. The ParFEMapper and…
We present an efficient B-spline finite element method (FEM) for cloth simulation. While higher-order FEM has long promised higher accuracy, its adoption in cloth simulators has been limited by its larger computational costs while…
We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on solvers…
An expandable local and parallel two-grid finite element scheme based on superposition principle for elliptic problems is proposed and analyzed in this paper by taking example of Poisson equation. Compared with the usual local and parallel…
Computer representations of three-dimensional (3D) geometries are crucial for simulating systems and processes in engineering and science. In medicine, and more specifically, biomechanics and orthopaedics, obtaining and using 3D geometries…
In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. Mixed generalized multiscale finite element method (GMsFEM)…