Studies and Solvers Updates

COMSOL Multiphysics® version 5.6 includes faster and more memory-lean multicore and cluster computing, new Domain Decomposition functionality, a new eigenvalue solver, and more. Learn about all of the updates relating to studies and solvers below.

Performance Improvements for Multicore and Cluster Computing

COMSOL Multiphysics® version 5.6 includes several performance improvements for the solution process. In particular, the memory requirements are reduced for Jacobian matrix assembly as well as for the algebraic multigrid preconditioner. The reduction is significant for both multicore and cluster computing. Furthermore, the most important smoothers used in the multigrid method are now more efficient, in particular for cluster computing.

As an illustration of the improvement, consider the following CFD benchmark of an Ahmed Body featuring turbulent flow. The model used in the benchmark has a refined mesh, as compared to the Application Gallery version, with 6.3 million degrees of freedom on a 16-node cluster. In this comparison, COMSOL Multiphysics® version 5.5 update 3 and version 5.6 are installed on a cluster where each node has 48 cores (2x Intel® Xeon® Platinum 8260 24 cores). The solvers used in the comparison are the algebraic multigrid solver (SA-AMG) as a preconditioner to GMRES with the Symmetrically Coupled Gauss-Seidel smoother (denoted MG in the comparison graphs). In addition, the overlapping Domain Decomposition (Schwarz) method is used as a preconditioner to GMRES with the multigrid method as a domain solver (denoted DD). The graphs below show the performance as computation time vs. number of nodes and memory usage vs. number of nodes.

A 3D model of an Ahmed body, visualized with a metallic sheen, and yellow, green, turquoise, and blue streamlines, and a white mesh around it. Ahmed body benchmark model Streamlines around the Ahmed Body and mesh in a vertical cross section.
A chart of time from 0 to 1800 seconds vs. number of nodes from 1 to 16 and blue lines for COMSOL Multiphysics version 5.5 update 3 and yellow lines for version 5.6. Wall-clock computation time comparison Wall-clock computation time for a refined version of the Ahmed Body benchmark model.
A chart of memory from 0 to 5000 MB vs. number of nodes from 1 to 16 and blue lines for COMSOL Multiphysics version 5.5 update 3 and yellow lines for version 5.6. Physical memory use comparison Physical memory use for a refined version of the Ahmed Body benchmark model.

Absorbing Boundary Condition for Domain Decomposition

In COMSOL Multiphysics® version 5.6, it is possible to select Absorbing boundary condition for the domain boundaries used by the Domain Decomposition method. This is useful for solving the Helmholtz equation, in particular for acoustics analysis, and can be used for both the nonoverlapping Schur-based and overlapping Schwarz-based Domain Decomposition methods. It is capable of solving larger wave problems than was possible in previous versions. The new methods are foremost intended for cluster computing.


A car cabin model with acoustic fields represented bu red, white, and blue. Car cabin acoustics model Car cabin acoustics analysis for 5 kHz solved with the new Absorbing boundary condition for the Domain Decomposition (Schur) method. The model has 30 million degrees of freedom, which are split into 10 domains. The wall-clock computation time is 2900 sec. and the memory peak is 118 GB when using 10 cluster nodes each with 48 cores (2x Intel® Xeon® Platinum 8260 24 cores).

FEAST: A New Eigenvalue Solver

COMSOL Multiphysics® version 5.6 comes with an interface for FEAST, which is a solver designed to find eigenvalues within an ellipse-shaped contour in the complex plane. It supports the usual symmetric or nonsymmetric formulations in COMSOL Multiphysics®. The method further supports automatic estimation of the number of eigenvalues within the contour, important for robustness and performance. One important aspect of FEAST is that different linear systems of equations are solved for each quadrature point along the contour and these problems are independent. Utilizing cluster computing, it is possible to use FEAST in parallel for improved performance.

New Preconditioner for Navier—Stokes Equations

A new preconditioner, Block Navier-Stokes, for CFD is added in COMSOL Multiphysics® version 5.6. It is based on classical methods like SIMPLE and SIMPLEC. The method makes it possible to solve for the velocity and pressure equation separately, even in the case of incompressible flow. This in turn makes it possible to use standard multigrid techniques with SOR or SOR Line smoothers. A reduction of the CPU-time up to 50% can be obtained compared to earlier versions. The method is implemented on the discrete level and can therefore be combined with several formulations including turbulence models and pseudo time stepping.

New Option for GMRES: Reuse of the Krylov Space

The popular iterative solver GMRES has a new option in COMSOL Multiphysics® version 5.6: Use GCRO-DR. When activated, and when the GMRES method restarts, instead of restarting from an empty Krylov space, the method reuses and improves the space already built up. This makes the method much more useful beyond the restart point, where before the convergence could often deteriorate badly at a restart. Now the restart can be seamless and with a much smaller penalty at restart in a typical situation. The Krylov space is also reused in the case of solving again, for nonlinear, parametric, or time-dependent solvers. The method stores twice as many vectors, in a similar fashion to FGMRES, but the extra storage only comes into play at a restart. At this point, it is typically worth the memory overhead to get a more robust behavior. The method can be seen as a lean and quick approximative full GMRES method or as an alternative to the methods TFQMR or BiCGStab, but without the somewhat unpredictable convergence characteristics that are common for these methods.


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