# Analysis Solvers

Three direct solvers and one iterative solver are available for the solution of the set of equations.

In finite element analysis, a problem is represented by a set of algebraic equations that must be solved simultaneously. There are two classes of solution methods: direct and iterative.

Direct methods solve the equations using exact numerical techniques. Iterative methods solve the equations using approximate techniques where in each iteration, a solution is assumed and the associated errors are evaluated. The iterations continue until the errors become acceptable.

The software offers the following choices:

 Automatic The software selects the solver based on the study type, analysis options, contact conditions, etc. Some options and conditions apply only to either Direct Sparse or FFEPlus. Direct Sparse Select the Direct Sparse: when you have enough RAM and multiple CPUs on your machine. when solving models with No Penetration contact. when solving models of parts with widely different material properties. For every 200,000 dof, you need 1GB of RAM for linear static analysis. The relationship between the number of equations (dofs) and memory requirement is not linear. For the most demanding data storage requirements (allocated size of matrices), RAM is set to be proportional to the second power of the number of equations (dofs). FFEPlus (iterative) The FFEPlus solver uses advanced matrix reordering techniques that makes it more efficient for large problems. In general, FFEPlus is faster in solving large problems and it becomes more efficient as the problem gets larger (up to the maximum memory available). For every 2,000,000 dof, you need 1GB of RAM. In general, the FFEPlus solver requires less RAM than the Direct Sparse and Intel Direct Sparse solvers. Large Problem Direct Sparse By leveraging enhanced memory-allocation algorithms, the Large Problem Direct Sparse solver can handle simulation problems that exceed the physical memory of your computer. If you initially select the Direct Sparse solver and due to limited memory resources it has reached an out-of-core solution, a warning message alerts you to switch to the Large Problem Direct Sparse. The Direct Sparse and Intel Direct Sparse solvers are more efficient than the FFEPlus and Direct Sparse solvers at taking advantage of multiple cores. Intel Direct Sparse The Intel Direct Sparse solver is available for static, thermal, frequency, linear dynamic, nonlinear studies, and topology studies. By leveraging enhanced memory-allocation algorithms and multi-core processing capability, the Intel Direct Sparse solver improves solution speeds for simulation problems that are solved in-core. For most cases, the Intel Direct Sparse solver is faster than the Direct Sparse. When the size of the model exceeds the maximum memory available, the Large Problem Direst Sparse is the most efficient solver. The Direct Sparse and Intel Direct Sparse solvers are more efficient at taking advantage of multiple cores.

## Choosing a Solver

The Automatic choice for a solver is the default option for Static, Frequency, Buckling, and Thermal studies.

In the case of multi-area contact problems, where the area of contact is found through several contact iterations, the Direct Sparse solver is preferred.

While all solvers are efficient for small problems (25,000 DOFs or less), there can be big differences in performance (speed and memory usage) in solving large problems.

If a solver requires more memory than available on the computer, then the solver uses disk space to store and retrieve temporary data. When this situation occurs, you get a message saying that the solution is going out of core and the solution progress slows down. If the amount of data to be written to the disk is very large, the solution progress can be extremely slow. In these cases (for static and nonlinear studies), use the Large Problem Direct Sparse.

 Size of the problem In general, FFEPlus is faster in solving problems with degrees of freedom (DOF) over 100,000. It becomes more efficient as the problem gets larger. Computer resources: Available RAM and number of CPUs (core or processors) The Direct Sparse solver requires about 10 times more RAM than the FFEPlus solver. It becomes faster with more memory available on your computer. The Large Problem Direct Sparse leverages multicore processing capability and improves solution speed for static and nonlinear studies. Material properties When the moduli of elasticity of the materials used in a model are very different (like Steel and Nylon), then iterative methods could be less accurate than direct methods. The direct solvers are recommended in such cases. Analysis features Analysis with No Penetration contacts and Bonded contacts enforced using constraint equations will typically solve faster with the direct solvers.

Depending on the study type, the following recommendations apply:

 Static Use the Direct Sparse and Large Problem Direct Sparse when you have enough RAM and multiple CPUS for solving: Models with No Penetration contact, especially when you turn on the friction effects. Models with parts that have widely different material properties. Mixed-mesh models For a linear static analysis, the Direct Sparse solver requires 1GB of RAM for every 200,000 degrees of freedom (dof). The iterative FFEPlus solver is less demanding on memory (approximately 2,000,000 dof / 1GB of RAM). Frequency and Buckling Use the FFEPlus solver to calculate any rigid body modes. A body without any restraints has six rigid body modes. Use the Direst Sparse and Intel Direst Sparse solvers for: Considering the effect of loading on the natural frequencies Models with parts that have widely different material properties. Models where incompatible mesh is bonded using constraint equations. Adding soft springs to stabilize inadequately supported models (buckling studies). Simulation uses the Subspace iteration method as the eigenvalue extraction method for the Direst Sparse solver, and the Lanczos method for the FFEPlus and Large Problem Direct Sparse solvers. It is more efficient to use Lanczos with iterative solvers like FFEPlus. Subspace can utilize the back and forth substitution of the Direct (Sparse) solvers within its iteration loop to evaluate the eigenvectors (only needs to decompose the matrix once.) That is not possible with iterative solvers. Thermal Thermal problems have one degree of freedom (DOF) per node, and hence their solution is usually much faster than structural problems of the same number of nodes. For very large problems (larger than 500.00 dofs), use the FFEPlus solver. Nonlinear For Nonlinear studies of models that have more than 50,000 degrees of freedom, the FFEPlus solver is more effective in giving a solution in a smaller amount of time. The Large Problem Direct Sparse solver can handle cases where the solution is going out of core.

## Solver Status

The Solver Status window appears when you run a study. In addition to progress information, it displays:

• Memory usage
• Elapsed time
• Study-specific information such as degrees of freedom, number of nodes, number of elements
• Solver information such as solver type
• Warnings

The Intel Direct Sparse solver does not provide a solver progress report status.

All studies that use the FFEPlus (iterative) solver (except frequency and buckling) let you access the convergence plot and solver parameters. The convergence plot helps you visualize how the solution is converging. The solver parameters let you manipulate the solver iterations so that you can either improve accuracy or improve speed. You can either use the solver's preset values or change:

• Maximum number of iterations (P1)
• Stopping threshold (P2)

To improve accuracy, decrease the stopping threshold value. In slowly converging situations, you can improve speed by increasing the stopping threshold value or by decreasing the maximum number of iterations (with the understanding that the results accuracy can be affected.)

## Multicore Processing

The table lists the multicore processing specifications of simulation solvers for each Simulation license.

Solvers Simulation Licenses - Limited to Maximum of 8 Physical Cores Simulation Licenses - No Limit on Number of Physical Cores
• FFEPlus
• Intel Direct Sparse
• Direct Sparse
• Large Problem Direct Sparse
• Intel Network Sparse
• Simulation Xpress
FFEPlus is the only solver option for Simulation Xpress.