> How do I compute the exponential of a matrix easily in deal.ii, with the > least amount of fuss (I can't find a function in the documentation that > does this)?
Coming back to the original question of how to solve an ODE x'=Ax: if A is the result of some PDE discretization, people don't usually go the route of matrix exponentiation because even if A is sparse, exp(A) is dense. This is true even if you compute exp(A) through the eigenvalue/eigenvector decomposition since you have to store O(n) eigenvectors of length n if you want to integrate to long times. An alternative, of course, is to just use one of the usual time stepping schemes, i.e. approximate the evolution of x(t) through algorithms like the (explicit or implicit) Euler method, Crank-Nicolson, BDF2, or Runge Kutta. I imagine you must have thought of this before, so it would be interesting to know why you thought that this wouldn't work? Best W. ------------------------------------------------------------------------- Wolfgang Bangerth email: [email protected] www: http://www.math.tamu.edu/~bangerth/ _______________________________________________ dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
