Nonlinear preconditioned conjugate gradient and least-squares finite elements
An extension of the authors' least-squares formulation for nonlinear first order systems of differential equations is presented. The similarity of the element matrices with the standard Galerkin approach is still retained. However, since the least-squares method is used, this formulation yields to a symmetric self-adjoint matrix. Since the solution scheme adopted is the nonlinear preconditioned conjugate gradient algorithm, a special preconditioner is constructed. The numerical analyses presented considers the steady inviscid compressible flow equation as model problems. Comparisons include element-by-element implementations of conjugate gradients and steep descent algorithms with several preconditioners as an iterative driver and nonlinear conjugate gradients. Although the authors' preconditioner is insensitive to the mesh size, the comparisons made seems to favour the Jacobi conjugate gradient iterative driver. However, the problems solved are still too small to clarify what is the best solution strategy.
steady inviscid compressible flow equation
scientific article; zbMATH DE number 4030909