Domain Decomposition for Adaptive hp Finite Element Methods

A highly parallelizable domain decomposition solution technique for adaptive hp finite element methods is developed. The technique uses good partitioning strategies and a subspace decomposition based preconditioned itera- tive solver, Two level orthogonalization is used to obtain a reduced system which is preconditioned by a coarse grid operator. Numerical results show fast cOIl\'er- gence for the iterative solver and good control of the condition number (less than 16 for meshes with spectral orders up to 8).