Related papers: A two-scale approach for efficient on-the-fly oper…
Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…
We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite difference/element discretizations of the Laplace equation. Using local Fourier…
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…
The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that…
This work introduces an adaptive mesh refinement technique for hierarchical hybrid grids with the goal to reach scalability and maintain excellent performance on massively parallel computer systems. On the block structured hierarchical…
Vectorization is increasingly important to achieve high performance on modern hardware with SIMD instructions. Assembly of matrices and vectors in the finite element method, which is characterized by iterating a local assembly kernel over…
The FE$^2$ homogenization algorithm for multiscale modeling iterates between the macroscale and the microscale (represented by a representative volume element) till convergence is achieved at every increment of macroscale loading. The…
The research in parallel machine scheduling in combinatorial optimization suggests that the desirable parallel efficiency could be achieved when the jobs are sorted in the non-increasing order of processing times. In this paper, we find…
In this paper, we combine the multiscale flnite element method to propose an algorithm for solving the non-stationary Stokes-Darcy model, where the permeability coefflcient in the Darcy region exhibits multiscale characteristics. Our…
This paper presents a 55-line code written in python for 2D and 3D topology optimization (TO) based on the open-source finite element computing software (FEniCS), equipped with various finite element tools and solvers. PETSc is used as the…
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…
We design and analyze an iterative two-grid algorithm for the finite element discretizations of strongly nonlinear elliptic boundary value problems in this paper. We propose an iterative two-grid algorithm, in which a nonlinear problem is…
Shuffling strategies for stochastic gradient descent (SGD), including incremental gradient, shuffle-once, and random reshuffling, are supported by rigorous convergence analyses for arbitrary within-epoch permutations. In particular, random…
We introduce a family of bi-grid schemes in finite elements for solving 2D incompressible Navier-Stokes equations in velocity and pressure $(u,p)$. The new schemes are based on projection methods and use two pairs of FEM spaces, a sparse…
This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…
A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…
An efficient $hp$-multigrid scheme is presented for local discontinuous Galerkin (LDG) discretizations of elliptic problems, formulated around the idea of separately coarsening the underlying discrete gradient and divergence operators. We…
This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…
Massive MIMO is widely considered as a key enabler of the next generation 5G networks. With a large number of antennas at the Base Station, both spectral and energy efficiencies can be enhanced. Unfortunately, the downlink channel…
Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…