Reduced order computation of 2D elastodynamic Green's functions in layered soil using a low-rank tensor approximation

TL;DR

This paper introduces a low-rank tensor approximation method using Greedy Tucker Approximation to efficiently compute 2D elastodynamic Green's functions in layered soils, significantly reducing computational costs.

Contribution

It develops a novel reduced order modeling approach employing GTA and PGD techniques for efficient Green's function computation in layered media.

Findings

Substantial memory reduction achieved

Faster computation times demonstrated

High accuracy validated against direct methods

Abstract

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 demanding and memory intensive. This paper presents a reduced order modeling strategy based on the Greedy Tucker Approximation (GTA), which incrementally constructs a low-rank representation of the Green's tensor through rank-one enrichments obtained via a Proper Generalized Decomposition (PGD)-type alternating least squares procedure. A Petrov-Galerkin formulation is employed to improve convergence and approximation accuracy. The resulting multi-dimensional tensor, expressed in terms of one-dimensional basis functions and a compact core, achieves substantial reductions in memory requirements. The methodology is demonstrated for two cases: a soil layer on rigid bedrock and a layered halfspace. Different separable dimensions are considered to capture various combinations of source and receiver configurations, frequencies, and material parameters. Results are validated against those obtained with the direct stiffness method and computation times and memory requirements are compared.