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Physics Informed Meshing for Accelerating the 3D Indirect Boundary Element Method Computation of Imaginary Part of Green’s Function at the Source

Description: 

There are some unusual boundary value problems which appear when emergent theories generate new questions. Such is the case of Diffuse Field Theory in Dynamic Elasticity. Theory posits that within such a field, the average directional energy densities, really the power spectra, are proportional to the corresponding imaginary parts of Green’s function at the source. For a given problem, the system’s Green’s function shares some properties with the classical elastic counterpart of the homogeneous full space; while the real part diverges at the source, the imaginary part is smooth. It is the basic building block to model energy ratios in layered medium. The H/V spectral ratio is a good example. The half-space with flat layers allows for a semi analytical solution. To deal with lateral inhomogeneities, the spectral element method has been used successfully. On the other hand, the Indirect Boundary Element Method (IBEM), formulated in the frequency domain, requires discretized boundaries with elements whose sizes decrease as frequency increases. This approach results in a significant growth in the number of equations, posing computational challenges.

To alleviate the burden, we developed an adaptive IBEM based on the physics of wave diffraction. It appears a viable alternative to use large discretization region and elements for low frequencies when diffraction is very strong, and small region and element sizes for large frequencies when geometrical effects prevail. Moreover, we account for distant elements that may contribute, if conveniently collimated, to the energy budget at the selected point. This fast, adaptive 3D IBEM is aimed to compute the imaginary part of Green’s function for a layer over an elastic half-space with a smooth laterally varying interface. For this problem, we found the IBEM solution accurate once it is calibrated with the imaginary part of Green’s tensor at the free surface. This solution, based on the principle of equipartition of energy, is well known. This work was partially supported by DGAPA-UNAM Project IN105523. J. G. González is supported by the UNAM Postdoctoral Program (POSDOC).

Session: Numerical Modeling in Seismology: Theory, Algorithms and Applications - I

Type: Oral

Date: 4/17/2025

Presentation Time: 08:15 AM (local time)

Presenting Author: Francisco

Student Presenter: No

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