SOLV Equation solver

SOLV Description Unit Default

VAL Selection of equation solver 1 Direct Skyline Solver

(Gauss/ Cholesky) 2 Iterative Sparse Solver 3 Direct Sparse LDL Solver

4 Direct Parallel Sparse Solver (PARDISO)

− 3

For solving the equation systems of the Finite-Element problem, SOFiSTiK pro- vides a number of solvers. Which solver is used best depends highly on the type of the system and requires knowledge of relevant system parameters. Following types are available:

• Direct Skyline Solver (Gauss/Cholesky)

This is the classical solver of the FE-Method. The current implementation works best on a skyline oriented matrix. The storage needed depends on the internal optimization of the node numbers and may become quite large for 3D structures.

• Iterative Solver (Conjugate Gradients)

One advantage of the iterative solver lies in its reduced requirements for storage, but it may also provide reduced computing time compared to the previous two types especially in case of large volume structures.

• Direct Sparse Solver

These types of solvers correspond to state of technology. A quite efficient version based on the work of DAVIS[5] is available as well as a direct parallel

solver PARDISO.

The advantage of the direct solvers is especially given in case of multiple right hand sides, as the effort for solving them is very small compared to the trian- gulization of the equation system. Thus they are the first choice for any dynamic analysis or in case of many load cases.

In order to minimize computational effort, the solvers need an optimized se- quence of equation numbers. This optimization step is usually performed during system generation. The programs SOFIMSHA/C by default always create a se- quence which is suitable for the direct sparse solver (3). The solvers (1) or (2) however require a skyline oriented numbering which may be obtained using the option (CTRL OPTI 1) or (CTRL OPTI 2) during system generation. The correct setting will be checked and a warning will be issued in case a correct numbering is not available.

The iterative (CTRL SOLV 2) and the parallel sparse solver (CTRL SOLV 4) can be run in parallel providing an additional reduction in computing time. A paral- lelization basically requires a license of type ”HISOLV”. More information about parallelization can be found in subsection 3.3.2 describing the input parameter (CTRL CORE).

The equation solvers are selected using the parameter (CTRL SOLV). The first value defines the type of the solver, followed by optional additional parameters.

SOLV Description Unit Default VAL 1 Direct Skyline Solver (Gauss/ C-

holesky)

− !

No additional parameters are required. However it is mandatory to optimize the equation numbers in SOFIMSHA/C using (CTRL OPTI 1) or (CTRL OPTI 2) in order to minimize computation time as well as storage requirements.

Iterative equation solver

SOLV Description Unit Default

VAL 2 Iterative equation solver − !

V2 Maximum number of iterations − *

V3 Tolerance in numeric digits (5 to 15) − * V4 Type of preconditioning:

0 Diagonal Scaling (not recom- mended)

1 Incomplete Cholesky 2 Incomplete Inverse

− 1

V5 Threshold value of preconditioning − * V6 Maximum bandwidth in preconditioning − *

The iterative solver uses a conjugate gradient method in combination with pre- conditioning. For the preconditioning, following variants are supported:

• Diagonal scaling (V4=0)

Although this is the fastest method with the least memory requirements, it will need a considerable high amount of iterations and is therefore not rec- ommended in most cases.

• Incomplete Cholesky (V4=1)

This type of preconditioning performs a partial triangulization of the input matrix. Compared to a full triangulization with the Cholesky method, the Incomplete Cholesky saves time by ignoring the so called Fill-In during de- composition.

• Incomplete Inverse (V4=2)

This type of preconditioning is generally inferior to the Cholesky method. This applies to the convergence-rate as well as the time required for com-

puting the inverses. It shows however better performance in case of more densely populated matrices (Recommended threshold V5: 0.01).

For any kind of preconditioning the number of matrix entries taken into account during preconditioning can be reduced either by giving a relative threshold value at V5 or via a maximum bandwidth size at V6. The optimum choice depends on the type of the structure and may only be found by some tests.

Hint

The correctness of the solution of the iterative solver depends primarily on the tolerance threshold. Therefore, changing the default setting V3 is not recommended. In any case the analyst should carry out a proper assess- ment of the computation results.

Direct Sparse LDL Solver (Default)

SOLV Description Unit Default

VAL 3 Direct Sparse LDL Solver − !

Additional parameters are not required. The mesh generators SOFiMSHA/C generate by default an equation numbering required for this type of solver which minimizes the so-called Fill In of the matrix.

PARDISO - direct parallel sparse solver

SOLV Description Unit Default

WERT 4 Direct parallel sparse solver − !

This solver PARDISO uses processor optimized high performance libraries from the Intel Math Kernel Library MKL. It usually provides the least computing times. It does not require an a priori optimization of the equation numbers during sys- tem generation. Hence, the equation optimization in SOFiMSHA/C could also be deactivated using (CTRL OPTI 0) in order to save memory during system generation. On the other hand however, this solver does not allow reusing the factorized stiffness matrix in other programs. Thus, a usage in combination with the program ELLA is not possible.

Further options

CTRL SOLV 0 suppresses the solution of the system. This is a useful feature to check the effective system loads.

STEU SOLV 999 prevents a rebuild of the stiffness matrix within a load case loop in each step.