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Accurately solving PDEs with localised features requires refined meshes that adapt to the solution. Traditional numerical methods, such as finite elements, are linear in nature and often ineffective for such problems, as the mesh is not…
The permeability of complex porous materials can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as…
The convergence and numerical analysis of a low memory implementation of the Orthogonal Matching Pursuit greedy strategy, which is termed Self Projected Matching Pursuit, is presented. This approach renders an iterative way of solving the…
Recently, graphics processors (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage…
Matrix-free geometric multigrid solvers for elliptic PDEs that have been discretised with Higher-order Discontinuous Galerkin (DG) methods are ideally suited to exploit state-of-the-art computer architectures. Higher polynomial degrees…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…
Energy system optimization models are increasing in scope and resolution, yielding large and challenging linear programs. For a long time, the standard way to address such problems has relied on shared-memory interior-point methods (IPM),…
Traditional approaches based on finite element analyses have been successfully used to predict the macro-scale behavior of heterogeneous materials (composites, multicomponent alloys, and polycrystals) widely used in industrial applications.…
Achieving strongly symmetric stress approximations for linear elasticity problems in high-contrast media poses a significant computational challenge. Conventional methods often struggle with prohibitively high computational costs due to…
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…
Discrete Fracture Network models are largely used for very large scale geological flow simulations. For this reason numerical methods require an investigation of tools for efficient parallel solutions on High Performance Computing systems.…
Volumetric spline parameterization and computational efficiency are two main challenges in isogeometric analysis (IGA). To tackle this problem, we propose a framework of computation reuse in IGA on a set of three-dimensional models with…
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…
Reconstruction of object or scene surfaces has tremendous applications in computer vision, computer graphics, and robotics. In this paper, we study a fundamental problem in this context about recovering a surface mesh from an implicit field…
Real time application of deep learning algorithms is often hindered by high computational complexity and frequent memory accesses. Network pruning is a promising technique to solve this problem. However, pruning usually results in irregular…
In this chapter we will give an insight into modern sparse elimination methods. These are driven by a preprocessing phase based on combinatorial algorithms which improve diagonal dominance, reduce fill-in, and improve concurrency to allow…
We present a novel parallel algorithm for cloth simulation that exploits multiple GPUs for fast computation and the handling of very high resolution meshes. To accelerate implicit integration, we describe new parallel algorithms for sparse…
In this work, we formulate and analyze a geometric multigrid method for the iterative solution of the discrete systems arising from the finite element discretization of symmetric second-order linear elliptic diffusion problems. We show that…
In this paper, we describe efficient MapReduce simulations of parallel algorithms specified in the BSP and PRAM models. We also provide some applications of these simulation results to problems in parallel computational geometry for the…