Improving the Numerical Simulation of an Airflow Problem with the BlockCGSI Algorithm
Carlos Balsa (FEUP)Michel Dayde (ENSEEIHT/IRIT)
Jose Laginha Palma (FEUP)
Daniel Ruiz (ENSEEIHT/IRIT)
Marianna Braza (IMFT/CNRS)
Abstract:
Partial spectral information associated with the smallest eigenvalues
can be used to improve the solution of consecutive linear systems
of equations, namely in the simulation of time-dependent partial
differential equations, where at each time step there are several systems
with the same spectral properties to be solved. We propose to perform
a partial spectral decomposition with the BlockCGSI algorithm in the
first time step, and exploit this information to improve the convergence
of the Conjugate Gradient algorithm in the solution of the following linear
systems. We describe in summary the BlockCGSI algorithm, that is
a combination of the block Conjugate Gradient (blockCG) with the Inverse
Subspace Iteration. Then, we validate the accelerating strategy in
the simulation of the flow around an airplane wing, where the Conjugate
Gradient is accelerated through the deflation of the starting residual.
Keywords:
Large Scale Simulations in all areas of Engineering and Science, Numerical Methods (Linear algebra), Numerical Methods (PDE)
