Abstract
There are many ways to solve space–time linear parabolic partial differential equations by using the boundary element method (BEM). In general, standard techniques make use of an incremental strategy. In this paper we propose a novel alternative of efficient non-incremental solution strategy for that kind of models. The proposed technique combines the use of the BEM with a proper generalized decomposition (PGD) that allows a space–time separated representation of the unknown field within a non-incremental integration scheme.
Highlights
The boundary element method (BEM) allows efficient solution of partial differential equations whose kernel functions are known
We proposed recently a technique able to construct, in a way completely transparent for the user, the separated representation of the unknown field involved in a partial differential equation
If instead of applying the proper generalized decomposition just discussed, one performs a standard incremental solution, P dD models, d 1⁄41, 2, 3, must be solved (P being the number of time steps, i.e. P 1⁄4 Tmax=Dt)
Summary
The boundary element method (BEM) allows efficient solution of partial differential equations whose kernel functions are known. Separated representations were already applied for solving transient models in the context of finite element discretizations [4,5,6,7,8,9,10], but they never have been used in the BEM framework, and certainly in this context the main advantage is the possibility of defining non-incremental strategies as well as the possibility of avoiding the use of space–time kernels. In principle, this technique seems specially adapted for solving transient problems involving extremely small time steps.
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