The MSC Sinda Thermal Library contains two basic types of steady state solver – iterative and direct. Iterative solvers include SNSOR and STDSTL and employ methods akin to the Gauss Seidel Method. Direct solvers include SSSPM and SSQMR, employing direct linear equation solvers (sparse matrix method or method of quasi-minimized residuals).

Usually, SNSOR is the default steady state solver, and uses successive over-relaxation to accelerate convergence. SNSOR almost always works well for linear and mildly nonlinear models. Control constant DAMPD is the over-relaxation parameter. By default, DAMPD is unspecified (or zero), so SNSOR computes it automatically. The user can impose over-relaxation by setting 1 < DAMPD < 2 or under-relaxation with 0 < DAMPD < 1.

If one-way conductors are present in the model, over-relaxation is suppressed (the automatic method requires a symmetrical matrix). This slows convergence, but is otherwise harmless.

SNSOR linearizes radiation, and this can cause the built in over-relaxation computation to go haywire, resulting in unstable divergence (Infinity or NaN in the solution). Setting the over-relaxation parameter manually (with DAMPD) usually resolves this problem. Starting with DAMPD = 1.5, try various values. Usually, an optimum value can be found for the fastest model convergence. If extreme nonlinearity exists in the model, under-relaxation may be necessary. Radiation nonlinearity usually is not this extreme.

STDSTL does not linearize radiation (solving fourth-order polynomials instead), so does not suffer from the divergence problem. However, the STDSTL extrapolation method has an overly aggressive default setting (EXTLIM = 50), and this tends to cause convergence problems too.

For very large plate-like models, SSSPM (sparse matrix) may be a better choice. Solid 3D models are not very sparse. Models with enclosure radiation are not very sparse. Plate-like spacecraft models do tend to be sparse, because radiation to space does not make the matrix non-sparse. SSSPM solutions with radiation often require under-relaxation with 0 < DAMPD < 1. Sometimes, the NNGSPM constant must be set to a larger value (default is 15). This controls the size of the array used to store the sparse matrix.

For very large 3D solid-like models, SSQMR (quasi-minimized residuals) may be the best choice. Like SSSPM, SSQMR may require 0 < DAMPD < 1 (under-relaxation) if radiation is an important part of the model.

For convergence, DRLXCA and ARLXCA specify the allowable temperature change between iterations. When this is solved, system energy balance checks (BALENG) are performed. Nodal balances (BENODE) are performed when the system balance is satisfied. The energy balance checks are not carried out unless the temperature convergence has already been achieved.