Related papers: An object oriented parallel finite element scheme …
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…
There is increasing interest in using multicore processors to accelerate stream processing. For example, indexing sliding window content to enhance the performance of streaming queries is greatly improved by utilizing the computational…
We describe a methodology for designing efficient parallel and distributed scientific software. This methodology utilizes sequences of mechanizable algebra--based optimizing transformations. In this study, we apply our methodology to the…
Manapy is a parallel, unstructured, finite-volume based solver for the solution of partial differential equations (PDE). The framework is written using Python, it is object-oriented, and is organized in such a way that it is easy to…
Neural surrogate solvers of partial differential equations (PDEs) promise dramatic speedups over numerical methods, especially in scenarios requiring many solves. However, current accuracy-based evaluations do not fully consider two central…
Deep neural networks with large model sizes achieve state-of-the-art results for tasks in computer vision (CV) and natural language processing (NLP). However, these large-scale models are too compute- or memory-intensive for…
The problem of finding the solution of Partial Differential Equations (PDEs) plays a central role in modeling real world problems. Over the past years, Multigrid solvers have showed their robustness over other techniques, due to its high…
Harnessing modern parallel computing resources to achieve complex multi-physics simulations is a daunting task. The Multiphysics Object Oriented Simulation Environment (MOOSE) aims to enable such development by providing simplified…
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…
This paper presents a framework that supports the implementation of parallel solutions for the widespread parametric maximum flow computational routines used in image segmentation algorithms. The framework is based on supergraphs, a special…
In this paper, we investigate the combination of multigrid methods and neural networks, starting from a Finite Element discretization of an elliptic PDE. Multigrid methods use interpolation operators to transfer information between…
This paper presents a methodology and software tools for parametric design of complex architectural objects, called digital or algorithmic forms. In order to provide a flexible tool, the proposed design philosophy involves two open source…
This article introduces a general purpose framework and software to approximate partial differential equations (PDEs). The sparsity patterns of finite element discretized operators is identified automatically using the tools from…
We develop all of the components needed to construct an adaptive finite element code that can be used to approximate fractional partial differential equations, on non-trivial domains in $d\geq 1$ dimensions. Our main approach consists of…
Graphics Processing Units (GPUs) are high performance co-processors originally intended to improve the use and quality of computer graphics applications. Once, researchers and practitioners noticed the potential of using GPU for general…
Neural operators aim to learn mappings between infinite-dimensional function spaces, but their performance often degrades on complex or irregular geometries due to the lack of geometry-aware representations. We propose the Finite Element…
In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware…
We present direct logarithmically optimal in theory and fast in practice algorithms to implement the tensor product high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. They…
Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and…
In this article, we introduce, a novel open-source framework designed for efficient parallel computation of projections in tomography leveraging either multiple CPU cores or GPUs. This framework efficiently implements forward and back…