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. |
• | Numeric selectors are set by selector = number. |
AUTOSTAGE type: Logical 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 type: Numeric default: 0.5(steady state), 0.1(time dependent)
Steady state: 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.
Time dependent: Specifies the maximum change in one timestep of any nodal variable derived from a steady-state equation. Changes larger than this amount will cause the timestep to be cut.
CUBIC type: Logical 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 type: Numeric 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 type: Logical 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 type: Logical default: Off
Disables the automatic timestep control. The timestep is fixed at the value given in the TIME section. (In most cases, this is not advisable, as it is difficult to choose a single timestep value that is both accurate and efficient over the entire time range of a problem. Consider modifying the ERRLIM control instead.)
HYSTERESIS type: Numeric 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 type: Logical 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 type: Numeric 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 type: Numeric 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 type: Numeric default: 0
Selects the Eigenvalue solver and specifies the desired number of modes. The default is not to run an Eigenvalue problem.
NEWTON type: Numeric default: (5/changelim)+40 (steady_state)
default: 1 (time-dependent)
Overrides the default maximum Newton iteration limit.
NONLINEAR type: Logical default: Automatic
Selects the nonlinear (Newton-Raphson) solver, even if the automatic detection process does not want it.
NONSYMMETRIC type: Logical default: Automatic
Selects the nonsymmetric Lanczos conjugate gradient solver, even if the automatic detection process does not want it.
NOTIFY_DONE type: Logical default: Off
Requests that FlexPDE emit a beep and a "DONE" message at completion of the run.
NRMINSTEP type: Numeric 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 type: Numeric default: 0.1
Sets the minimum acceptable residual improvement in Newton-Raphson backtracking of steady-state solutions.
ORDER type: Numeric 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 type: Numeric 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 type: Logical default: On
Use matrix preconditioning in conjugate-gradient solutions. The default preconditioner is the diagonal-block inverse matrix.
PREFER_SPEED type: Logical default: On
This selector chooses parameters for nonlinear time-dependent problems that result in greatest solution speed for well-behaved problems. Equivalent to NEWTON=1, REMATRIX=Off.
PREFER_STABILITY type: Logical default: Off
This selector chooses parameters for nonlinear time-dependent problems that result in greatest solution stability in ill-behaved problems. Equivalent to NEWTON=5, REMATRIX=On.
QUADRATIC type: Logical default: On
Selects use of quadratic Finite Element basis. Equivalent to ORDER=2.
RANDOM_SEED type: Numeric default: random
Specifies the seed for random number generation. May be used to create repeatable solution of problems using random numbers.
REINITIALIZE type: Logical 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.
REMATRIX type: Logical default: Off
Forces a re-calculation of the Jacobian matrix for each step of the Newton-Raphson iteration in nonlinear problems. The matrix is also recomputed whenever the solution changes appreciably, or when the residual is large. Replaces NRMATRIX in previous version.
STAGES type: Numeric 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 type: Numeric 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 type: Numeric 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.
THREADS type: Numeric default: 1
Selects the number of worker threads to use during the computation. This control is useful in increasing computation speed on computers with multiple shared-memory processors. FlexPDE does not support clusters. See "Using Multiple Processors"for more information.
TNORM type: Numeric 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.
UPFACTOR type: Numeric default: 1
Multiplier on upwind diffusion terms. Larger values can sometimes stabilize a marginal hyperbolic system.
UPWIND type: Logical 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 type: Logical 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 type: Numeric 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.
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