相关论文: GCA-$\mathcal{H}^2$ matrix compression for electro…
We present a fast algorithm that constructs a data-sparse approximation of matrices arising in the context of integral equation methods for elliptic partial differential equations. The new algorithm uses Green's representation formula in…
The efficiency of boundary element methods depends crucially on the time required for setting up the stiffness matrix. The far-field part of the matrix can be approximated by compression schemes like the fast multipole method or…
The Adaptive Cross Approximation (ACA) method is widely used to approximate admissible blocks of hierarchical matrices, or H-matrices, from discretized operators in the boundary integral method. These matrices are fully populated, making…
A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select…
Boundary element methods for the Helmholtz equation lead to large dense matrices that can only be handled if efficient compression techniques are used. Directional compression techniques can reach good compression rates even for…
The acoustic wave equation is solved in time domain with a boundary element formulation. The time discretisation is performed with the generalised convolution quadrature method and for the spatial approximation standard lowest order…
We propose a new analytical approximation to the $\chi^2$ kernel that converges geometrically. The analytical approximation is derived with elementary methods and adapts to the input distribution for optimal convergence rate. Experiments…
Boundary integral equations lead to dense system matrices when discretized, yet they are data-sparse. Using the $\mathcal{H}$-matrix format, this sparsity is exploited to achieve $\mathcal{O}(N\log N)$ complexity for storage and…
A method for the kernel-independent construction of $\mathcal{H}^2$-matrix approximations to non-local operators is proposed. Special attention is paid to the adaptive construction of nested bases. As a side result, new error estimates for…
In this paper, we demonstrate how GPU-accelerated BEM routines can be used in a simple black-box fashion to accelerate fast boundary element formulations based on Hierarchical Matrices (H-Matrices) with ACA (Adaptive Cross Approximation).…
Directional interpolation is a fast and efficient compression technique for high-frequency Helmholtz boundary integral equations, but it requires a very large amount of storage in its original form. Algebraic recompression can significantly…
The evaluation of elastodynamic Green's functions across numerous source-receiver locations, frequencies, and material properties, particularly in the context of parametric studies or boundary element computations, is computationally…
This paper introduces a dynamic, error-bounded hierarchical matrix (H-matrix) compression method tailored for Physics-Informed Neural Networks (PINNs). The proposed approach reduces the computational complexity and memory demands of…
The inference and training stages of Graph Neural Networks (GNNs) are often dominated by the time required to compute a long sequence of matrix multiplications between the sparse graph adjacency matrix and its embedding. To accelerate these…
The architecture of the brain is too complex to be intuitively surveyable without the use of compressed representations that project its variation into a compact, navigable space. The task is especially challenging with high-dimensional…
Gaussian process regression techniques have been used in fluid mechanics for the reconstruction of flow fields from a reduction-of-dimension perspective. A main ingredient in this setting is the construction of adapted covariance functions,…
In this work, we study the accuracy and efficiency of hierarchical matrix ($\mathcal{H}$-matrix) based fast methods for solving dense linear systems arising from the discretization of the 3D elastodynamic Green's tensors. It is well known…
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…
In order to deal with the scaling problem of volumetric map representations we propose spatially local methods for high-ratio compression of 3D maps, represented as truncated signed distance fields. We show that these compressed maps can be…
We present the Composite Operator Method (COM) as a modern approach to the study of strongly correlated electronic systems, based on the equation of motion and Green's function method. COM uses propagators of composite operators as building…