Related papers: Solving Sparse Finite Element Problems on Neuromor…
Applications in robotics or other size-, weight- and power-constrained autonomous systems at the edge often require real-time and low-energy solutions to large optimization problems. Event-based and memory-integrated neuromorphic…
Neuromorphic hardware is based on emulating the natural biological structure of the brain. Since its computational model is similar to standard neural models, it could serve as a computational acceleration for research projects in the field…
Large sparse symmetric linear systems appear in several branches of science and engineering thanks to the widespread use of the finite element method (FEM). The fastest sparse linear solvers available implement hybrid iterative methods.…
Robust fitting of geometric models is a fundamental task in many computer vision pipelines. Numerous innovations have been produced on the topic, from improving the efficiency and accuracy of random sampling heuristics to generating novel…
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…
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…
We analyze a new framework for expressing finite element methods on arbitrarily many intersecting meshes: multimesh finite element methods. The multimesh finite element method, first presented in [40], enables the use of separate meshes to…
In this paper, we present a new immersed finite element scheme for solving elliptic interface problems on unfitted meshes by combining the skeletal finite element method (FEM) with the standard FEM. The skeletal FEM is used for the…
The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…
We develop a sparse multiscale operator-adapted wavelet decomposition-based finite element method (FEM) on unstructured polygonal mesh hierarchies obtained via a coarsening procedure. Our approach decouples different resolution levels,…
Recent research has demonstrated the usefulness of neural networks as variational ansatz functions for quantum many-body states. However, high-dimensional sampling spaces and transient autocorrelations confront these approaches with a…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…
We discuss how to implement the linear finite element method for solving the Poisson equation. We begin with the data structure to represent the triangulation and boundary conditions, introduce the sparse matrix, and then discuss the…
Neuromorphic engineering combines the architectural and computational principles of systems neuroscience with semiconductor electronics, with the aim of building efficient and compact devices that mimic the synaptic and neural machinery of…
We consider the problem of computing a sparse binary representation of an image. To be precise, given an image and an overcomplete, non-orthonormal basis, we aim to find a sparse binary vector indicating the minimal set of basis vectors…
It has long been realized that neuromorphic hardware offers benefits for the domain of robotics such as low energy, low latency, as well as unique methods of learning. In aiming for more complex tasks, especially those incorporating…
This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the…
Floorplanning is the first stage of VLSI physical design. An effective floorplanning engine definitely has positive impact on chip design speed, quality and performance. In this paper, we present a novel mathematical model to characterize…
The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far either suffer from lack of accuracy and/or are limited to very small sizes of the…
We present a design-scheme for ultra-low power neuromorphic hardware using emerging spin-devices. We propose device models for 'neuron', based on lateral spin valves and domain wall magnets that can operate at ultra-low terminal voltage of…