Classical numerical methods (Finite difference, Finite volume, Finite Element,... rely on a mesh to solve the problem. The Finite Element Method (FEM)and Finite Volume Method (FVM) may be the most well-known members of these thoroughly developed mesh-based methods. In contrast, a comparably new class of numerical methods has been developed which approximates partial differential equations only based on a set of nodes without mesh.
We used to work on a method called global element.
This needs no mesh, but the physics principle is similar to FEM.
We solve 3D eddy currents with it on machines with about 1k RAM.
However, handling geometrical features, other methods are better.
Then we used finite difference to capture geometry better.
Again we solved practical problems with it reasonable - this time in CP/M up to 64k, then DOS. Stair-casing is inconvenient, FEM is best for closed domains.
For open domains BEM is needed. To have it all, I'm for hybrid FEM-BEM. I'd recommend Trefftz method for BEM bacause it fits FEM with common energy concepts.
We solved some problems with this approach where infinite elements failed. To extend it completely, ad FEM-BEM-global element hybrid looks the winner. I'm not aware anyone coded this.
In general when you get simple geometries very simple flow then any method works....but when it comes to complex geometries with a complex flow in a complex configuration...with large deformation and discontinuities or singularities then...meshfree methods are the solution.
Hybrid methods like FEM-BEM or FEM SPH....are a good strategy to solve equations
Absolutely.
To be considered also accuracy, CPU time, hardware and effort.
11th International SPHERIC SPH Workshop; Technical University of Munich, Germany, 14-16 June, 2016
Link to workshop website: www.spheric2016.tum.de.
1-day SPHERIC Training Day, 13 June 2016.
12th International SPHERIC SPH Workshop,
Universidade de Vigo - Ourense, Spain 2017 including Training Day.
International Conference on Boundary Element and Meshless Techniques
11-13 July 2017
Radisson Blu Hotel, Bucharest, Romania
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