Related papers: Solving Sparse Finite Element Problems on Neuromor…
We introduce a fast mesh-based method for computing N-body interactions that is both scalable and accurate. The method is founded on a particle-particle--particle-mesh P3M approach, which decomposes a potential into rapidly decaying…
Fiber-reinforced soft biological tissues are typically modeled as hyperelastic, anisotropic, and nearly incompressible materials. To enforce incompressibility a multiplicative split of the deformation gradient into a volumetric and an…
This work delves into solving the two dimensional Poisson problem through the Finite Element Method which is relevant in various physical scenarios including heat conduction, electrostatics, gravity potential, and fluid dynamics. However,…
Achieving fast and reliable temporal signal encoding is crucial for low-power, always-on systems. While current spike-based encoding algorithms rely on complex networks or precise timing references, simple and robust encoding models can be…
A particle-in-cell algorithm is derived with a canonical Poisson structure in the formalism of finite element exterior calculus. The resulting method belongs to the class of gauge-compatible splitting algorithms, which exactly preserve…
Multiple scale homogenization problems are reduced to single scale problems in higher dimension. It is shown that sparse tensor product Finite Element Methods (FEM) allow the numerical solution in complexity independent of the dimension and…
In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…
Parallel finite element algorithms based on object-oriented concepts are presented. Moreover, the design and implementation of a data structure proposed are utilized in realizing a parallel geometric multigrid method. The ParFEMapper and…
Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…
A finite element method is presented to compute time harmonic microwave fields in three dimensional configurations. Nodal-based finite elements have been coupled with an absorbing boundary condition to solve open boundary problems. This…
Since the 1950s, soft ionic devices have evolved from individual components to an expanding library of sensors, actuators, signal transmitters, and processors. However, integrating these components into complex, multi-functional systems…
Programming recurrent spiking neural networks (RSNNs) to robustly perform multi-timescale computation remains a difficult challenge. To address this, we describe a single-shot weight learning scheme to embed robust multi-timescale dynamics…
Neuromorphic sampling is a bioinspired and opportunistic analog-to-digital conversion technique, where the measurements are recorded only when there is a significant change in the signal amplitude. Neuromorphic sampling has paved the way…
This paper presents a mini immersed finite element (IFE) method for solving two- and three-dimensional two-phase Stokes problems on Cartesian meshes. The IFE space is constructed from the conventional mini element, with shape functions…
In recent years, a number of finite element methods have been formulated for the solution of partial differential equations on complex geometries based on non-matching or overlapping meshes. Examples of such methods include the fictitious…
In this work we formally derive and prove the correctness of the algorithms and data structures in a parallel, distributed-memory, generic finite element framework that supports h-adaptivity on computational domains represented as…
Spiking Neural Networks (SNNs) are inspired by the sparse and event-driven nature of biological neural processing, and offer the potential for ultra-low-power artificial intelligence. However, realizing their efficiency benefits requires…
We develop a sparse hierarchical $hp$-finite element method ($hp$-FEM) for the Helmholtz equation with variable coefficients posed on a two-dimensional disk or annulus. The mesh is an inner disk cell (omitted if on an annulus domain) and…
The finite-element method is a preferred numerical method when electromagnetic fields at high accuracy are to be computed in nano-optics design. Here, we demonstrate a finite-element method using hp-adaptivity on tetrahedral meshes for…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…