Re: [deal.II] Mass matrix for a distributed vector problem

[Robert Spartus]

Dear all,

Thanks for the insightful discussion on the integrating issue. Wolfgang, I
guess your last argument is the same as you gave in one of your fantastic
lectures?

Incidentally, do you have any ideas on how to solve the singularity of the
mass matrix in this vector-valued problem?

Bests,
Bob

On Friday, 12 April 2019, Wolfgang Bangerth  wrote:

> On 4/12/19 1:55 PM, luca.heltai wrote:
> > Wolfgang, is that true also for mass matrices? I’d agree with you for
> > stiffness matrices, but I’d surprised this worked ok for mass
> > matrices as well.
>
> I'm pretty sure. The theory goes like this: instead of computing the
> matrix and rhs using the bilinear and linear forms
>
>a(u,v) = f(v)
>
> you're committing a variational crime by using quadrature instead of
> integrals:
>
>\tilde a(u,v) = \tilde f(v)
>
> You then need to quantify the error due to this crime, and it turns out
> that in order to not lose a convergence order, all you have to do is
> compute the integrals via quadrature to the same convergence order as
> for the overall finite element method. So, if you use elements of degree
> k, you get O(h^k) in the energy norm, and you only need to integrate
> matrix and rhs terms accurately enough to order O(h^k), which you can do
> by using k+1 Gauss points in each coordinate direction.
>
> Best
>   W.
>
> --
> 
> Wolfgang Bangerth  email: bange...@colostate.edu
> www: http://www.math.colostate.edu/~bangerth/
>
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[deal.II] Computation of Eigenvalues by Power Method with deal.ii

[illi]

I have the following code snippet for computing Eigenvalues using Power 
Method:
Vector x;
x = solution;
double v = 0.0;
PrimitiveVectorMemory> mem;
const EigenPower>::AdditionalData data(0.);
EigenPower<> ep(solver_control, mem, data);
ep.solve(v, system_matrix, x);
(where system_matrix is a SparseMatrix)

The code arises an* abort trap*. What is wrong?


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