Solution Controls

The following controls can be used in the SELECT section to modify the solution methods of FlexPDE.

Logical selectors can be turned on by selector = ON, or merely mentioning the selector.

Logical selectors can be turned off by selector = OFF.

AUTOSTAGE                        default: On

In STAGED problems, this selector causes all stages to be run consecutively without pause. Turning this selector OFF causes FlexPDE to pause at the end of each stage, so that results can be examined before proceeding.

CHANGELIM                        default: 0.5(steady state), 2.0(time dependent)

Specifies the maximum change in any nodal variable allowed on any Newton iteration step (measured relative to the variable norm).  In severely nonlinear problems, it may be necessary to force a slow progress toward the solution in order to avoid pathological behavior of the nonlinear functions.         

CUBIC                        default: Off

Use cubic Finite Element basis (same as ORDER=3).  The default is quadratic (ORDER=2).  Cubic basis creates a larger number of nodes, and sometimes makes the system more ill-conditioned.        

ERRLIM                        default: 0.002        

This is the primary accuracy control.  Both the spatial error control XERRLIM the temporal error control TERRLIM are set to this value unless over-ridden by explicit declaration.

[Note: ERRLIM is an estimate of the relative error in the dependent variables.  The solution is not guaranteed to lie within this error.  It may be necessary to adjust ERRLIM or manually force greater mesh density to achieve the desired solution accuracy.]        

FIRSTPARTS                        default: Off

By default, FlexPDE integrates all second-order terms by parts, creating the surface terms represented by the Natural boundary condition.  This selector causes first-order terms to be integrated by parts as well. Use of this option may require adding terms to Natural boundary condition statements.        

FIXDT                        default: Off

Disables the automatic timestep control.  The timestep is fixed at the value given in the TIME section.        

HYSTERESIS                        default: 0.5

Introduces a hysteresis in the decay of spatial error estimates in time-dependent problems. The effective error estimate includes this fraction of the previous effective estimate added into the current instantaneous estimate.  This effect produces more stable regridding in most cases.

ICCG                        default: On

Use Incomplete Choleski Conjugate-Gradient in symmetric problems. This method usually converges much more quickly. If ICCG=OFF or the factorization fails, then the Orthomin method will be used.        

ITERATE                        default: 1000 (steady-state)

                       default: 500(time-dependent)

Primary conjugate gradient iteration limit.  This is the count at which convergence-coercion techniques begin to be applied. The actual hard maximum iteration count is 4*ITERATE.

LINUPDATE                        default: 5

In linear steady-state problems, FlexPDE repeats the linear system solution until the computed residuals are below tolerance, up to a maximum of LINUPDATE passes.        

MODES                        default: 0

Selects the Eigenvalue solver and specifies the  desired number of modes.  The default is not to run an Eigenvalue problem.                

NEWTON                        default: (5/changelim)+40

Overrides the default maximum Newton iteration limit.        

NONLINEAR                        default: Automatic

Selects the nonlinear (Newton-Raphson) solver, even if the automatic detection process does not want it.                

NONSYMMETRIC                default: Automatic

Selects the nonsymmetric Lanczos conjugate gradient solver, even if the automatic detection process does not want it.        

NOTIFY_DONE                        default: Off        

Requests that FlexPDE emit a beep and a "DONE" message at completion of the run.                

NRMATRIX                        default: 5

Sets the maximum number of Newton-Raphson iterations before recomputing the coupling matrix in steady-state solutions. The matrix is recomputed whenever the solution changes appreciably, or when the residual is large.

NRMINSTEP                        default: 0.009

Sets the minimum fraction of the computed stepsize which will be applied during Newton-Raphson backtracking.  This number only comes into play in difficult nonlinear systems.  Usually the computed step is unmodified.

NRSLOPE                        default: 0.1

Sets the minimum acceptable residual improvement in Newton-Raphson backtracking of steady-state solutions.

NRUPDATE                        default: 5

Sets the maximum number of Newton-Raphson steps in each timestep in nonlinear time dependent problems. The default (5) seems to give the best balance between cost and stability.  Well-behaved nonlinear problems may run more quickly with 1.  This selector is set automatically by the PREFER_SPEED and PREFER_STABILITY selectors.

NRUPFIT                        default: Off

"ON" requests that FITs and SAVEs be recalculated at each Newton Iteration of nonlinear time-dependent problems.  Prior to version 2.20e, these items were computed once in each timestep.  The default condition uses only one Newton step per timestep, so this selector is useful only if NRUPDATE is also set.

ORDER                        default: 2

Selects the order of finite element interpolation (2 or 3).  The selectors QUADRATIC and CUBIC are equivalent to ORDER=2 and ORDER=3, respectively.        

OVERSHOOT                        default: 0.0005

Sub-iteration convergence control. Conjugate-Gradient solutions will iterate to a tolerance of OVERSHOOT*ERRLIM.  (Some solution methods may apply additional multipliers.)        

PRECONDITION                default: On

Use matrix preconditioning in conjugate-gradient solutions.  The default preconditioner is the diagonal-block inverse matrix.        

PREFER_SPEED                default: Off        

Sets control parameters for time dependent problems to the best balance for speedy completion of most problems.  Use PREFER_STABILITY for more difficult nonlinear problems.  PREFER_SPEED is equivalent to NRUPDATE=1, TNORM=2.

PREFER_STABILITY                default: On

Sets control parameters for time dependent problems to a slower but more stable configuration for difficult nonlinear problems.  PREFER_STABILITY is equivalent to NRUPDATE=3, TNORM=4. Well-behaved nonlinear problems may run more quickly using PREFER_SPEED.

QUADRATIC                        default: On        

Selects use of quadratic Finite Element basis. Equivalent to ORDER=2.

REINITIALIZE                        default: Off

Causes each Stage of a STAGED problem to be reinitialized with the INITIAL VALUES specifications, instead of preserving the results of the previous stage.        

STAGES                        default: 1

Parameter-studies may be run automatically by selecting a number of Stages. Unless the geometric domain parameters change with stage, the mesh and solution of one stage are used as a starting point for the next.

SUBSPACE                        default: MIN(2*modes,modes+8)

If MODES has been set to select an eigenvalue problem, this selector sets the dimension of the subspace used to calculate eigenvalues.        

TERRLIM                        default: 0.002        

This is the primary temporal accuracy control.  In time dependent problems, the timestep will be cut if the estimated relative error in time integration exceeds this value. The timestep will be increased if the estimated temporal error is smaller than this value. TERRLIM is automatically set by the ERRLIM control.

[Note: TERRLIM is an estimate of the relative error in the dependent variables. The solution is not guaranteed to lie within this error.  It may be necessary to adjust TERRLIM to achieve the desired solution accuracy.]        

TNORM                        default: 4

Error averaging method for time-dependent problems.  Timestep control is based on summed (2^TNORM) power of nodal errors.  Allowable values are 1-4. Use larger TNORM in problems with localized activity in large mesh.        

TORDER                        default: 2

Selects the order of the Backward Difference Formula for time integration. TORDER=1 is the classical backward Euler method.  TORDER=2 uses a quadriatic fit over two timesteps.  TORDER > 3 is not supported.        

UPFACTOR                        default: 1

Multiplier on upwind diffusion terms.  Larger values can sometimes stabilize a marginal hyperbolic system.        

UPWIND                        default: On

"Upwind" convection terms in the  primary equation variable.  In the presence of convection terms, this adds a diffusion term along the flow direction to stabilize the computation.        

VANDENBERG                        default: Off

Use Vandenberg Conjugate-Gradient iteration (useful if hyperbolic systems fail to converge).  This method essentially solves (AtA)x = (At)b instead of Ax=b.  This squares the condition number and slows convergence, but it makes all the eigenvalues positive when the standard CG methods fail.        

XERRLIM                        default: 0.002        

This is the primary spatial accuracy control.  Any cell in which the estimated relative spatial error in the dependent variables exceeds this value will be split (unless NODELIMIT is exceeded).  XERRLIM is set automatically by the  ERRLIM selector. 

[Note: XERRLIM is an estimate of the relative error in the dependent variables. The solution is not guaranteed to lie within this error.  It may be necessary to adjust XERRLIM or manually force greater mesh density to achieve the desired solution accuracy.]