[R-sig-dyn-mod] Question on Galerkin

[Rob Goedman]

Karline,

Thank you for your reply. 

As you suggested, over the weekend I've read the ReacTran vignettes and package to see if that is a possible starting point. I've also looked at colnewR.f  and bvpSolver.R as in our simple case of a beam/pipe, aren't we solving an ODE? Its the separation (and link) between finite differences (FD) and finite elements (FE) I'm indeed struggling with.

Until that is resolved or better understood, I see 2 'packages':

1)	A FD 'replacement' for what I do now primarily in Mathematica (learning/experimenting/solving with the Galerkin method).

	The objective is to make the 'first 3 chapters' of FEM books more accessible, e.g. Smith & Griffith or Zienkiewicz, Taylor & Zhu.

2)	A FE capability where users can define material properties and geometry for initially (3D) beam/pipe elements.

	The first objective is to develop this as an initial template to interface to existing FEM programs.

	A second objective is to include 2nd order effects (I use the onset of lateral buckling for my work). Or flexural-torsional buckling in architecture ('kip' in Dutch). 
	I'm not sure if and how these play in for fluid dynamics, an area that is important to my work, I just haven't spend enough time on it.

This does not cover your goal of adding FEM to R, although the 2nd might be a useful first step.

Thanks again for your feedback.

Regards,
Rob


On Apr 30, 2011, at 10:45 AM, Soetaert, Karline wrote:

> Rob,
> 
> The collocation method that is already in R is for solving boundary value problems (1-D), it is implemented in R-package bvpSolve.
> 
> Another R-package ReacTran, may be more related to FEM, but this uses finite differences, not finite elements, and it is designed to approximate the diffusive-advective equation on very structured (1-D, 2-D, 3-D) grids. The functions of this package are used to convert the PDEs to ODEs which are then solved with specially-designed solvers from package deSolve (ode.1D,...ode.3D) or from package rootSolve. You may have a look at the ReacTran package to see how we do this.
> 
> I think that adding FEM  to R would be really nice and a very timely addition to the use of R for solving differential equations, and I really hope you will do this.
> 
> Karline
> 
> ________________________________
> 
> From: r-sig-dynamic-models-bounces at r-project.org on behalf of Rob Goedman
> Sent: Sat 4/30/2011 5:37 PM
> To: r-sig-dynamic-models at r-project.org
> Cc: Rob Goedman
> Subject: [R-sig-dyn-mod] Question on Galerkin
> 
> 
> 
> Hi,
> 
> As a (frequent) user of (simple, beams only) FEM I'm right now trying to dig a bit deeper into the underlying methods/concepts using Mathematica, R and several Fortran codes, e.g. Colorado School of Mines (Smith, Griffiths), our own developed toolset (both driven from R) and, on the side, several others (e.g. FEAPpv, Matrix Frame).
> 
> Recently I've been thinking about packaging our own toolset as an R package.
> 
> Before I do that, I've seen a reference to collocation in the 'Solving Differential Equations in R'  intro (page 6, top right, Bader & Ascher). I'm wondering if it is conceivable to add the method='Galerkin' to e.g. ode. Or is FEM/Galerkin considered so different or specific that this should not be contemplated?
> 
> Any feedback or pointers to books/intro's are very much appreciated.
> 
> Regards,
> Rob Goedman
> 
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