Proper orthogonal decomposition (POD) is a method for obtaining a basis for representing physical phenomena and has been used in reduced order models for fast analysis. To apply POD to large-scale problems, distributed memory parallel computing, in which parallel processes are allocated to each partitioned subdomain, is effective. On the other hand, Local POD, which obtains a basis for each decomposed subdomain, has been proposed to improve the computational efficiency of POD. Against this background, we propose a method to independently set subdomains where the basis is acquired and subdomains where parallel processes are allocated. Through its application to diffusion equations, we discuss the computing efficiency and parallel computational performance.

This study proposes an end-to-end pipeline for constructing acoustic digital twins directly from multi-view photographs by coupling a neural implicit surface and a finite element method with an immersed boundary formulation. Geometry is learned as a Signed Distance Function (SDF) by using a neural implicit surface-based photogrammetry, NeuS, and injected into a Volume Penalization (VP)-based finite element formulation of the Helmholtz equation using an approximated Heaviside mask. Verification on rigid-sphere scattering shows good agreement with theoretical solutions and grid convergence. A feasibility study with actual images demonstrates plausible scattering fields on a 100³ hexahedral mesh. The framework can generalize to other SDF-based photogrammetry and enables image-to-simulation workflows for acoustic digital twins.