Nested grids ILU-decomposition (NGILU)

Multilevel ILU decomposition

In this paper, the multilevel ILU (MLILU) decomposition is introduced. During an incomplete Gaussian elimination process new matrix entries are generated such that a special ordering strategy yields distinct levels. On these levels, some smoothing steps are computed. The MLILU decomposition exists and the corresponding iterative scheme converges for all symmetric and positive deenite matrices. ...

On the robustness of ILU smoothers on triangular grids

Article history: Received 10 August 2015 Received in revised form 21 January 2016 Accepted 5 February 2016 Available online 22 March 2016

Legendre–Gauss–Lobatto Grids and Associated Nested Dyadic Grids

Legendre-Gauss-Lobatto (LGL) grids play a pivotal role in nodal spectral methods for the numerical solution of partial differential equations. They not only provide efficient high-order quadrature rules, but give also rise to norm equivalences that could eventually lead to efficient preconditioning techniques in high-order methods. Unfortunately, a serious obstruction to fully exploiting the po...

Algebraic Domain Decomposition Method for Unstructured Grids

Lightweight Nested Inheritance in Layer Decomposition

Software is often constructed as a stack of layers where a sublayer extends its superlayer. Such extension of layers requires extension of mutually recursive classes that form a layer. Furthermore, a class within a layer often inherits from another class within the same layer, and this inheritance relation is preserved in the sublayer. Supporting these features in a type-safe object-oriented la...