This article proposes a novel high-performance computing approach for the prediction of the
temperature field in powder bed fusion (PBF) additive manufacturing (AM) processes. In …

Several previous experiments showed that the leapfrog–hopscotch and the adapted Dufort–
Frankel methods are the most efficient among the explicit and stable numerical methods to …

We collected 20 explicit and stable numerical algorithms for the one-dimensional transient
diffusion equation and analytically examined their consistency and convergence properties …

We utilize the travelling-wave Ansatz to obtain novel analytical solutions to the linear
diffusion–reaction equation. The reaction term is a function of time and space …

This article proposes a novel high-performance computing approach for the prediction of the
temperature field in powder bed fusion (PBF) additive manufacturing processes. In contrast …

The time-dependent diffusion equation is studied, where the diffusion coefficient itself
depends simultaneously on space and time. First, a family of novel, nontrivial analytical …

Based on many previous experiments, the most efficient explicit and stable numerical
method to solve heat conduction problems is the leapfrog-hopscotch scheme. In our last …

This paper focuses on simulating nonlinear transient heat transfer in multilayer walls under
varying heat loads, using efficient numerical algorithms. The algorithms employed are …

This work addresses the fast macroscale modelling of powder bed fusion for metallic
materials. The main available approaches are analysed and applied on a typical benchmark …

We systematically test families of explicit adaptive step size controllers for solving the
diffusion or heat equation. After discretizing the space variables as in the conventional …