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The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…
Computation of a signal's estimated covariance matrix is an important building block in signal processing, e.g., for spectral estimation. Each matrix element is a sum of products of elements in the input matrix taken over a sliding window.…
Smoothing filter is the method of choice for image preprocessing and pattern recognition. We present a new concurrent method for smoothing 2D object in binary case. Proposed method provides a parallel computation while preserving the…
In this work, we consider alternative discretizations for PDEs which use expansions involving integral operators to approximate spatial derivatives. These constructions use explicit information within the integral terms, but treat boundary…
In this paper, we propose a novel reordering scheme to improve the performance of a Laplacian Mesh Smoothing (LMS). While the Laplacian smoothing algorithm is well optimized and studied, we show how a simple reordering of the vertices of…
Extract-Transform-Load (ETL) handles large amount of data and manages workload through dataflows. ETL dataflows are widely regarded as complex and expensive operations in terms of time and system resources. In order to minimize the time and…
As quantum computers continue to improve and support larger, more complex computations, smart control hardware and compilers are needed to efficiently leverage the capabilities of these systems. This paper introduces a novel approach to…
In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of…
In this article, we introduce a fast and memory efficient solver for sparse matrices arising from the finite element discretization of elliptic partial differential equations (PDEs). We use a fast direct (but approximate) multifrontal…
We improve the performance of multigrid solvers on many-core architectures with cache hierarchies by reorganizing operations in the smoothing step to minimize memory transfers. We focus on patch smoothers, which offer robust convergence…
Unstructured-mesh based numerical algorithms such as finite volume and finite element algorithms form an important class of applications for many scientific and engineering domains. The key difficulty in achieving higher performance from…
We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…
Matrix-free finite element implementations of massively parallel geometric multigrid save memory and are often significantly faster than implementations using classical sparse matrix techniques. They are especially well suited for…
Often, machine learning applications have to cope with dynamic environments where data are collected in the form of continuous data streams with potentially infinite length and transient behavior. Compared to traditional (batch) data…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post-processing step in…
We present numerical experiments for geophysics electromagnetic (EM) modeling based upon high-order edge elements and supervised $h+p$ refinement approaches on massively parallel computers. Our high-order $h+p$ refinement strategy is based…
Cache partitioning techniques have been successfully adopted to mitigate interference among concurrently executing real-time tasks on multi-core processors. Considering that the execution time of a cache-sensitive task strongly depends on…
We propose new sequential sorting operations by adapting techniques and methods used for designing parallel sorting algorithms. Although the norm is to parallelize a sequential algorithm to improve performance, we adapt a contrarian…
In this paper we develop a simple finite element method for simulation of embedded layers of high permeability in a matrix of lower permeability using a basic model of Darcy flow in embedded cracks. The cracks are allowed to cut through the…