33 research outputs found
A solver combining reduced basis and convergence acceleration with applications to non-linear elasticity
International audienceAn iterative solver is proposed to solve the family of linear equations arising from the numerical computation of nonâlinear problems. This solver relies on two quantities coming from previous steps of the computations: the preconditioning matrix is a matrix that has been factorized at an earlier step and previously computed vectors yield a reduced basis. The principle is to define an increment in two subâsteps. In the first subâstep, only the projection of the unknown on a reduced subspace is incremented and the projection of the equation on the reduced subspace is satisfied exactly. In the second subâstep, the full equation is solved approximately with the help of the preconditioner. Last, the convergence of the sequences is accelerated by a wellâknown method, the modified minimal polynomial extrapolation. This algorithm assessed by classical benchmarks coming from shell buckling analysis. Finally, its insertion in path following techniques is discussed. This leads to nonâlinear solvers with few matrix factorizations and few iterations