#Comsol 5.3 stokes manual#
#Comsol 5.3 stokes full#

#Comsol 5.3 stokes full#

The near-field part of the matrix is sparse and requires much less memory to store and solve for than the full matrix. Both of these are exposed to the so-called near-field part of the matrix. Two preconditioners are provided: the Sparse Approximate Inverse (SAI) and Direct Preconditioner. These alternatives correspond to two different versions of the adaptive cross approximation method, which is a fast matrix multiplication method based on far-field approximations. This enables matrices to be compressed using so-called ACA or ACA+ compression.

To mitigate this, support is provided for iterative solvers based on fast matrix-vector multiplication. In other words, the solution time increases dramatically with problem size. The solution time for this direct solver is approximately proportional to the cube of the number of degrees of freedom (DOF) in the problem.

This is useful for applications not well suited for finite element method (FEM) modeling. This Euler Bump benchmark model now uses the new adaptive mesh refinement functionality in COMSOLР’В Multiphysics Р’В®.Р”Р„pplication Library path for an application using new adaptive mesh refinement: CFD_Module/High_Mach_Number_Flow/euler_bump Fast Iterative Solver for Boundary Element Method ProblemsР”Р„ dense direct solver is now available for solving problems best solved through the boundary element method (BEM). This means that there is no need for the user to add any Convert features to the meshing sequence. The Regular refinement and Longest refinement methods now also automatically convert the mesh to triangles or tetrahedrons when needed. This is possible because adapted meshes are built with the Reference feature, which preserves the original mesh sequence together with the new Size Expression meshing feature. Improvements have further led to the Mesh initialization method now being able to perform adaptation on meshes other than just the triangular and tetrahedral types. Moreover, the L2-error (of the PDE residual) estimate is now also available for postprocessing. The adaptation functionality and error estimation have also been unified such that the error estimates used by the adaptation method are now available as dependent variables to be used for postprocessing the results. See the Mesh Updates page for more details. Alternatively, the Size Expression node can be added to a meshing sequence in the Model Builder in order to vary element size throughout the modeling space using expressions. The Adapt feature refines your mesh based on either an expression for the error in your solution or by an expression for the desired mesh element size. To achieve this, two new meshing features have been introduced: Adapt and Size Expression.

#Comsol 5.3 stokes manual#

Furthermore, the resulting adapted meshes are now based on meshing features that make it possible to seamlessly switch from the automated solution process to manual adaptation when required. The h-adaptation algorithm for stationary, parametric, and eigenvalue problems has been revised so that you can save the intermediate solutions and meshes. The SA-AMG solver requires only one mesh level, which is far easier to obtain.Р”Р„daptation Integrated with Meshing Sequences and Error Estimation This difference in dimensions makes it difficult to efficiently mesh the air domain together with the smaller parts and components, which would be made even more difficult if three meshes of different sizes are to be created. The SA-AMG solver only requires one mesh level, making the meshing process much easier and the solving process much more robust for large problems and 'difficult' geometries.Р”Р‡or example, in the fluid-structure interaction model of a solar panel (in the image), the struts and beams supporting the panels are small in comparison to the air domain surrounding it.

Use of the alternative geometric multigrid (GMG) solver requires three mesh levels to be considered, which can create issues when trying to mesh and solve models with varying geometries of different sizes. The smoothed aggregation algebraic multigrid (SA-AMG) method has been extended to work with the specialized smoothers for CFD in COMSOLР’В Multiphysics Р’В®: SCGS, Vanka, and SOR Line. Browse all of the COMSOLР’В Multiphysics Р’В® version 5.3 updates relating to studies and solvers below. COMSOLР’В Multiphysics Р’В® version 5.3 includes a new solver for CFD simulations and a new solver for electromagnetic and corrosion boundary element method simulations.