Direct Linear Equation Solver

Linear equation solution is used in linear and nonlinear analysis. In nonlinear analysis Abaqus/Standard uses the Newton method or a variant of it, such as the Riks method, within which it is necessary to solve a set of linear equations at each iteration. The direct linear equation solver finds the exact solution to this system of linear equations (up to machine precision). The direct linear equation solver in Abaqus/Standard:

  • uses a sparse, direct, Gauss elimination method; and

  • often represents the most time consuming part of the analysis (especially for large models)—the storage of the equations occupies the largest part of the disk space during the calculations.

See Also
Iterative Linear Equation Solver
In Other Guides
Abaqus/Standard and Abaqus/Explicit Execution
Environment File Settings
Parallel Execution in Abaqus/Standard

ProductsAbaqus/Standard

The Sparse Solver

The direct sparse solver uses a “multifront” technique that can reduce the computational time to solve the equations dramatically if the equation system has a sparse structure. Such a matrix structure typically arises when the physical model is made from several parts or branches that are connected together; a spoked wheel is a good example of a structure that has a sparse stiffness matrix. Space frames and other structures modeled with beams, trusses, and shells often have sparse stiffness matrices. In contrast, a blocky structure—such as a single, solid, three-dimensional block (see Elastic-plastic line spring modeling of a finite length cylinder with a part-through axial flaw)—provides little opportunity for the sparse solver to reduce the computer time. For large blocky structures, the iterative linear equation solver may be more efficient (see Iterative Linear Equation Solver).

Input File Usage

Use the following option to use the default direct sparse solver:

STEP

Setting Controls for the Direct Linear Solver

The linear equation solver can optimize elimination of constraint equations associated with hard contact and hybrid elements. There are two potential undesirable side-effects associated with this option:

  • Possible small degradation of solution accuracy may adversely impact the nonlinear convergence behavior.

  • Possible minor performance degradation for models without hard contact constraints and/or hybrid elements.

Input File Usage

Use the following option to turn on constraint optimization:

SOLVER CONTROLS,  CONSTRAINT OPTIMIZATION