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GeoPDES: Software for Isogeometric Analysis

Posted November 8, 2010 at 11:09 by praveen (CFD, Numerical Analysis, Scientific Computing)
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Isogeometric Analysis is a relatively new approach proposed by T. J. R. Hughes and his group to combine CAD and finite element analysis. The basic idea is to use the same (finite) representations for the geometry and FEM solution space, mostly based on B-splines and NURBS. The major advantage is the exact representation of geometry in computer aided design and analysis. An excellent introduction is given in the book

Isogeometric Analysis: Toward Integration of CAD and FEA
...
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Flux computation in unstructured grids

Posted July 16, 2010 at 10:49 by praveen (CFD, Numerical Analysis, Scientific Computing)

Consider finite volume scheme on unstructured grids for the Euler equations.

Let n=(n_x,n_y,n_z) be normal to a cell face and whose magnitude is equal to face area. Let Q be the conserved vector. The finite volume update equation using forward Euler time discretization is

Q^{n+1}_j = Q^n_j - \Delta t \sum_{k \in N(j)} F(Q_j^n, Q_k^n, n_{jk})

Here n_{jk} is a normal vector pointing from current cell "j" into the neighbouring cell...
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Elmer and deal.ii

Posted July 9, 2010 at 09:48 by praveen (CFD, Numerical Analysis, Scientific Computing)

There are two PDE solvers that I came across recently which look good. Both are FEM based.

Elmer has a good gui and has many physical models already available. There is a good amount of manuals and tutorials available. To get all of them, check out the code from svn. It also has some ability to program your own solvers but this is not well documented. It is a good aid for teaching numerical methods. Windows executable can be downloaded from their website. There is also a Mac binary...
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Adjoint consistency of DG method

Posted July 8, 2010 at 11:54 by praveen (CFD, Numerical Analysis, Scientific Computing)

Adjoint Consistency Analysis of Discontinuous Galerkin Discretizations
SIAM J. Numer. Anal. Volume 45, Issue 6, pp. 2671-2696 (2007)
http://dx.doi.org/10.1137/060665117

This paper gives a notion of consistent adjoint discretizations for DG methods. However the definition seems to be restricted to smooth solutions only. For the case of a conservation law, they show that boundary conditions of the primal problem must be appropriate for the corresponding adjoint discretization...
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Research Assistant position available

Posted July 6, 2010 at 12:30 by praveen (CFD, Numerical Analysis, Scientific Computing)

I have recently posted an opening for a Research Assistant position available with me soon. For more information and how to apply, please see

http://math.tifrbng.res.in/~praveen
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