This paper presents an output-based error estimation and adaptation strategy for hybridized discontinuous Galerkin discretizations of firstand second-order systems of conservation laws. A discrete adjoint solution is obtained by a Schurcomplement solver similar to that used in the primal problem. An error estimate is obtained by computing the adjoint on an enriched solution space that consists ...

We present a preconditioner for saddle point problems which is based on an approximation of an implicit representation of the inverse of the saddle point matrix. Whereas this preconditioner does not require an approximation to the Schur complement, its theoretical analysis yields some interesting relationship to some Schurcomplement-based preconditioners. Whereas the evaluation of this new prec...

With the advent of detailed numerical models, computing runtime can become excessive. We propose the facilitation of an innovative multi-level inverse-based LU preconditioning approach to improve computational efficiency while processing EIT system matrices. This combines static reordering and scaling, controlled growth of the inverse of triangular factors and approximation of the Schurcompleme...

We introduce a method for constructing a polynomial preconditioner using a nonlinear least squares (NLLS) algorithm. We show that this polynomial-based NLLS-optimized (PBNO) preconditioner significantly improves the performance of 2-D continuous Galerkin (CG) and discontinuous Galerkin (DG) fluid dynamical research models when run in an implicit-explicit time integration mode. When employed in ...