arXiv subjects

Vibudha Lakshmi Keshava

Publications and source records attributed to Vibudha Lakshmi Keshava.

3 recordsLinked to original sources

arXiv2026

A 3D-ACA accelerated time domain boundary element method for elastodynamics using FMM and $\mathcal{H}$-matrix techniques

The time-domain Boundary Element Method (BEM) for linear elastodynamics with vanishing initial conditions is considered. Spatial discretization uses standard low-order boundary elements, while temporal discretization employs the generalized Convolution Quadrature (gCQ) method. The gCQ framework requires evaluating BEM matrices in the Laplace domain at several complex frequencies along a chosen contour, producing a three-dimensional tensor with one spatial matrix slice per frequency. To reduce storage and computational cost, a low rank approximation of the tensor is computed using 3D-Adaptive Cross Approximation (3D-ACA), extending the classical ACA to handle both the additional frequency dimension and the tensorial structure of elastodynamics. Within each frequency slice, the BEM matrices are further compressed using either the classical ACA algorithm using the $\mathcal{H}$-matrix approach or a Chebyshev interpolation based Fast Multipole Method (FMM). A comparative study of all proposed methods is carried out using two academic examples, and the structural vibration of an induction machine is analyzed.

math.NA↗

arXiv2025

Comparison of $\mathcal{H}$-matrix- and FMM-based 3D-ACA for a time-domain boundary element method

The homogeneous wave equation is solved by a time-domain boundary element method (BEM) using low-order shape functions for spatial, and the generalised convolution quadrature method (gCQ) by Lopez-Fernandez and Sauter for temporal discretisation. The three-dimensional array of BEM matrices according to a set of complex frequencies in Laplace domain is approximated by generalised Adaptive Cross Approximation (3D-ACA). Its rank is increased adaptively until a prescribed accuracy is reached, relying on a pure algebraic error criterion. The data slices for the selected frequency points are further processed by either the standard $\mathcal{H}$-matrices approach with ACA or by a fast multipole method (FMM). This paper compares both approaches with respect to their demands in storage and computing time. Both techniques are illustrated for calculating the sound scattered by an electric machine, for which the proposed algebraic compression techniques make time-domain BEM feasible for the first time.

math.NA↗

arXiv2025

Partial integration based regularization in BEM for 3D elastostatic problems: The role of line integrals

The Boundary Element Method (BEM) is a powerful numerical approach for solving 3D elastostatic problems, particularly useful for crack propagation in fracture mechanics and half-space problems. A key challenge in BEM lies in handling singular integral kernels. Various analytical and numerical integration or regularization techniques address this, including one that combines partial integration with Stokes' theorem to reduce hyper-singular and strong singular kernels to weakly singular ones. This approach typically assumes a closed surface, omitting the boundary integrals from Stokes' theorem. In this paper, these usually neglected boundary line integrals are introduced and their significance is demonstrated, first in a pure half-space problem, and then shown to be redundant in fast multipole method (FMM) based BEM, where geometry partitioning produces pseudo open surfaces.

math.NA↗