Decades ago, Paul Erdős used randomness to illuminate the vast and weird world of networks. Now mathematicians are making his ...

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 ...

Abstract: In this paper, we present a hybrid finite difference/finite volume method and we apply it to solve an automotive electromagnetic compatibility (EMC) problem. The principles of the hybrid ...

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 ...

This paper presents a numerical meshless approach for solving the two-dimensional Allen-Cahn equation, utilizing a radial basis function-compact finite difference (RBF-CFD) method in combination with ...

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 ...

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 ...

This contribution proposes two third-order numerical schemes for solving time-dependent linear and non-linear partial differential equations (PDEs). For spatial discretization, a compact fourth-order ...