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 ...

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

In this work, a finite volume formulation developed for two-dimensional models is extended to deal with axisymmetric models of heat conduction applications. This formulation uses a vertex centered ...

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 ...

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

In this work a Finite-Difference Frequency-Domain (FDFD) propagation method for complex urban environments is proposed. The formulation starts from the discretization of the Helmholtz equation for the ...

Beam is one of the common structures in engineering, with the development of technology, homogeneous beams no longer meet the needs of engineering structural design, for this reason, people have ...

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 ...