SPM_Regularization_Type

regularization type if all boundaries are Neumann-type

The PDEs solved in MESHFREE for the pressure are of the form \( \Delta p = f\) with the boundary conditions \( p=A\) (Dirichlet) or \( \frac{\partial p}{\partial n} = B\) (Neumann). If, for the whole domain, only Neumann-conditions are given, the arising linear sparse system is singular and has to be regularized. Default: SPM_Regularization_Type = 2 Type 1: Instead of solving \( {\bf A } \cdot {\bf x} = {\bf b}\), we solve the perturbed system \begin{align} \left( {\bf A } + \epsilon {\bf I} \right) \cdot {\bf x} = {\bf b} \end{align} where \( {\bf I}\) is the identity matrix Type 2: (all linear solvers but SAMG): Instead of solving \( {\bf A } \cdot {\bf x} = {\bf b}\), we solve the perturbed system \begin{align} \left( {\bf A } + \epsilon {\bf J} \right) \cdot {\bf x} = {\bf b} \end{align} where \( {\bf J}\) is a matrix that contains 1 in all entries. This amounts to weakly requiring that the sum of the result vector entries is zero, i.e. \( \sum {\bf x}_i = 0\) Type 2: (in the case LINEQN_solver_ScalarSystems is set to SAMG): SAMG aims to solve \( {\bf A } \cdot {\bf x} = {\bf b}\), subject to the condition \begin{align} {\bf x} \cdot {\bf 1} = 0 \end{align} where \( {\bf 1}\) is a vector that contains 1 in all entries. This may not work in case of an incompatible right hand side, set SPM_Regularization_Type = 1 then. Esilon can be adjusted in SPM_Regularization_Epsilon.
This item is referenced in:
SPM_Regularization_Epsilon adjust numerical parameter epsilon for the matrix regularizations
SPM_Regularization_Type regularization type if all boundaries are Neumann-type
Beta Latest release notes for the MESHFREE beta executables
All Complete release notes for the MESHFREE beta executables