An adapted plane waves method for heat conduction problems

Martins, NFM, and P. Mota. "An adapted plane waves method for heat conduction problems." Applied Mathematics and Computation. 415 (2022).


In this paper we construct a new set of basis functions for the numerical solution of nonhomogeneous heat conduction problems with Dirichlet boundary conditions and null initial data. These functions can be seen as Newtonian potentials of plane waves for the heat equation and satisfy a null initial condition. Density results for adapted waves will be established and several numerical simulations will be presented in order to discuss the accuracy and feasibility of the proposed method. An application of the method for heat problems with non null initial temperature will also be discussed.

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