AWE

Table 6-27: Valid AWE Properties
Property	Value	Default	Description
acceptshort	on \| off	on	If on, the solver accepts short intervals unconditionally
atol	scalar	0.001	Absolute tolerance for parameter sweep
aweassemble	all \| one	all	Either assemble all the needed matrices at once, or one at a time
awefunc	string \| vector of strings		Expression(s) used in the search algorithm
clist	String array		Provide values for constants as input parameters using a string array; for the corresponding constant names, use cname.
cname	String array		Provide names of constants as input parameters using a string array; for the corresponding constant values, use clist.
expeval	scalar \| numeric vector	range(0.1,0.1,0.9)	Where to check the error in each subinterval.
expsize	scalar	3	Number of terms in expansion.
exptype	pade \| taylor	pade	Use Padé or Taylor expansions to approximate the unknown.
keeplog	on \| off	off	Keep warnings in stored log.
minint	scalar	0	The shortest allowed subinterval length
minintactive	on \| off	off	If off, rtol times the parameter span is. used. If on, minint is used.
message	String		The log message from the last solution process.
outsollinearized	du \| u	du	Store the total solution (u) or deviation and linerization point (du), when storelinpoint=off.
plist	scalar \| numeric vector		Parameter list.
plot	on \| off	off	Plot while solving.
plotgroup	String	default	Plot group to use for plot while solving.
pname	vector of strings		Parameter names.
pout	plist \| psteps	plist	Output either the parameters in plist or the solution at the expansion points.
probesel	all \| none \| manual	all	The probes to compute.
probes	vector of strings		Probes to use when probesel=manual.
rtol	scalar	0.01	Relative tolerance for parameter sweep.
storelinpoint	on \| off	off	Whether to store the linearization point.

The AWE solver computes expansions of an underlying problem around certain parameter values. In the first step the largest and smallest values of plist are used as expansion points. Using these expansions, the values of one or more functions at intermediate parameter values are computed. If the two expansions give similar enough functional values at these internal points, the interval is accepted and no subdivisions of that particular interval are deemed necessary.

The property awefunc is used to specify the functionals of interest and the property expeval determines at which internal points these functionals are to be evaluated. The values for expeval are given relative the interval. That is, a value of 0.5 means that the functionals are evaluated at the midpoint of each interval. When the functional-values from the two expansions are compared, a check is performed to see if they fulfill the specified tolerances atol and rtol. If neither of the tolerances are fulfilled, the interval is bisected and the process is repeated for each subinterval. Before a bisection is performed a check is made to make sure that the new intervals are not shorter than the shortest allowed. By default the shortest allowed interval is given by the relative tolerance times the length of the interval defined by plist (when minintactive is set to off). If minintactive has been set to on the value of minint is the shortest interval allowed. If minint has been specified, the value of minintactive is on by default. The property acceptshort determines how to handle too short intervals. If acceptshort is set to off and a short interval is detected, the solver is interrupted with an error/warning. If acceptshort is set to on and a short interval is detected, the solver accepts the interval even if the tolerances have not been fulfilled.

In AWE several matrices are needed to compute each expansion. There are two options when it comes to assembling these matrices: With aweassemble set to all everything is assembled in a single call to the Xmesh. With aweassenble set to one, the matrices are assembled one at a time. The first option is faster but requires more memory.