spectral_galerkin_heat Documentation
A semi-analytical Spectral Galerkin model for efficiently solving the nonlinear heat equation on a fixed cuboid domain.
spectral_galerkin_heat resolves the transient thermal field of a scanning laser including phase change, evaporative cooling, and convection on cuboid domains. It drives the laser heat source directly from G-code. Linear diffusion is integrated analytically in a spectral eigenbasis, which removes the global algebraic solve of an implicit finite-element step and is implemented for CPU and GPU. On a single-pass laser scan it agrees with a high-fidelity finite-element reference to within 0.67% in relative \(L^2\) error (see Validation & Results).
Simulation of a laser path with spectral_galerkin_heat.
How to get started?
Start with the Theory & Physics (how the method works) and the Validation & Results (how it compares against analytical, finite-element, and existing work). The Examples then proceed from a short tutorial to a full non-linear run. See Installation to get the code.