In October 2024 I attended a workshop at Harvard University where mathematicians talked through the uses of artificial intelligence in their field. Most were less worried about the future of math than ...

Compared to the conventional high-order staggered-grid finite-difference method (C-SFD), the time–space domain dispersion-relation-based high-order staggered-grid finite-difference method (TS-SFD) can ...

FDModBiotCyl.jl simulates seismic wavefield by solving Biot dynamic poroelasticity equations using a staggered-grid finite-difference method. It assumes azimuthally symmetric wavefields in a ...

This paper presents a simple but effective and efficient approach to improve the accuracy and stability of the least-squares Monte Carlo method. The key idea is to construct an ansatz for the ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

What Are FEM, FDM and FVM? FEM, FDM and FVM differ from one another in important ways. Understanding these distinctions is key to selecting the method most appropriate for your purposes. The ...

Numerical simulation of three-dimensional (3D) seismic wavefields forms the basis of the research on the migration methods of 3D seismic data based on wave equations. Because the simulation precision ...

Abstract: Partial differential equations (PDEs) are ubiquitous in physics and engineering and used for understanding various physical phenomena, including heat, diffusion, fluid and electrodynamics, ...

Abstract: To model the responses of borehole electromagnetic sensing in complicated geological environments, the geometric multigrid preconditioned finite-difference frequency-domain (FDFD) method is ...

Finite Element Analysis, or FEA, is the simulation of a physical phenomenon using a numerical mathematic technique called the Finite Element Method, or FEM. This process is at the core of mechanical ...