Related papers: Efficient Fast Multipole Accelerated Boundary Elem…
In this paper, we present a numerical algorithm for the accurate and efficient computation of the convolution of the frequency domain layered media Green's function with a given density function. Instead of compressing the convolution…
There is a growing interest in custom spatial accelerators for machine learning applications. These accelerators employ a spatial array of processing elements (PEs) interacting via custom buffer hierarchies and networks-on-chip. The…
In this work we present an algorithm to construct an infinitely differentiable smooth surface from an input consisting of a (rectilinear) triangulation of a surface of arbitrary shape. The original surface can have non-trivial genus and…
Numeric modeling of electromagnetics and acoustics frequently entails matrix-vector multiplication with block Toeplitz structure. When the corresponding block Toeplitz matrix is not highly sparse, e.g. when considering the electromagnetic…
Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices…
The computational cost of the boundary-condition-enforced immersed boundary method (IBM) increases in the order of $\mathcal{O}(N^2)$ as the number of Lagrangian points, $N$, increases. This is due to the time-consuming calculation of the…
The presented paper concentrates on the boundary element method (BEM) for the heat equation in three spatial dimensions. In particular, we deal with tensor product space-time meshes allowing for quadrature schemes analytic in time and…
This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…
This work presents a multi-layered methodology for efficiently accelerating multimodal foundation models (MFMs). It combines hardware and software co-design of transformer blocks with an optimization pipeline that reduces computational and…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…
Standard finite element methods employ an element-wise assembly strategy. The element's contribution to the system matrix is formed by a loop over quadrature points. This concept is also used in fictitious domain methods, which perform…
Kernel matrix-vector multiplication (KMVM) is a foundational operation in machine learning and scientific computing. However, as KMVM tends to scale quadratically in both memory and time, applications are often limited by these…
A novel finite element method for the approximation of Maxwell's equations over hybrid two-dimensional grids is studied. The choice of appropriate basis functions and numerical quadrature leads to diagonal mass matrices which allow for…
Finding optimal solutions to combinatorial optimization problems is pivotal in both scientific and technological domains, within academic research and industrial applications. A considerable amount of effort has been invested in the…
This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective…
Numerical methods such as the Finite Element Method (FEM) have been successfully adapted to utilize the computational power of GPU accelerators. However, much of the effort around applying FEM to GPU's has been focused on high-order FEM due…
In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks…
In this paper, a Quadrature by Two Expansions (QB2X) numerical integration technique is developed for the single and double layer potentials of the Helmholtz equation in two dimensions. The QB2X method uses both local complex Taylor…
Large language models (LLMs) have been widely applied but face challenges in efficient inference. While quantization methods reduce computational demands, ultra-low bit quantization with arbitrary precision is hindered by limited GPU Tensor…
We present a new accelerated gradient-based method for solving smooth unconstrained optimization problems. The goal is to embed a heavy-ball type of momentum into the Fast Gradient Method (FGM). For this purpose, we devise a generalization…