Nonlinear Coupled Problems Solved by hpFEM
Abstract
A necessity to solve coupled problems arises in various fields of physics and engineering. The main aim of this work is to develop a general framework and software for simple solving of complex coupled problems and to investigate and compare various different approaches towards the solution. Namely we want to quantify benefits of monolithic discretization of the coupled problem (where all fields are discretized together into one matrix for each time level of the transient problem) with respect to the standard approach, where each field is resolved separately using values of the other fields from the previous time level for the nonlinear constants, when necessary. As an example of a real device we selected actuator, where magnetic field causes heating of certain parts and it results to its prolongation. It is used for precise positioning of various objects. Implementation is done using hpFEM method, which is extremely efficient for problems with complex behavior exhibiting singularities or boundary layers.
 Publication:

Numerical Analysis and Applied Mathematics ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics
 Pub Date:
 September 2011
 DOI:
 10.1063/1.3636994
 Bibcode:
 2011AIPC.1389.1948K
 Keywords:

 software (computers);
 partial differential equations;
 geometry;
 magnets;
 07.05.Hd;
 02.30.Jr;
 02.40.Xx;
 84.71.Ba;
 Data acquisition: hardware and software;
 Partial differential equations;
 Singularity theory;
 Superconducting magnets;
 magnetic levitation devices