User supplied subroutine

Figure 8 depicts our view of an ideal structure for an applications program. The boxes with the heavy borders represent those functions that are problem specific, while the light-border boxes represent those functions that can be relegated to problem-independent software. This structure is well-suited to problems that are mathematically either systems of nonlinear algebraic equations, ordinary differential equation initial or boundary value problems, or parabolic partial differential equations. In these cases the problem-independent mathematical software is usually written in the form of a subroutine that in turn calls a user-supplied subroutine to define the system of equations. Of course, the user must write the subroutine that defines his particular system of equations. However, that subroutine should be able to make calls to problem-independent software to return many of the components that are needed to assemble the governing equations. Specifically, such software could be called to return in-... 

The error tolerance EP is set to the value EP = Xy lE-6, which is certainly smaller than the attainable accuracy based on the approximate equation (2.5). Due to the PRINT statement in the user supplied subroutine the program output is long, and only a few iterations are shown in Table 2.1. 

The direct methods are not very efficient in terms of the number of function evaluations, but are robust, decreasing the objective function up to some extent in most cases. Requiring only one user supplied subroutine they are easy to use. 

The role of the input data NM, NX, NY and NP is obvious from the text and the remark lines, but the array T(NM,NX) of independent variables deserves some explanation. Each line of the array should contain all information that enables us to compute the value of the dependent variables for a sample paint at the current values of the parameters. Therefore, the module transfers the appropriate row of T(NM,NX) into the vector X(NX) for further use in the user supplied subroutine. This subroutine starting at line 900 computes the independent variables Y(NY) at the current parameters P(NP) and independent... 

PARAMETER ESTIMATES 2 NZ) CORRECTED VARIABLES FURTHER RESULTS PRINTED IN THE MODULE REM USER-SUPPLIED SUBROUTINES ... 

The module calls the user supplied subroutine starting at line 900 that evaluates the right hand sides of (5.1) at the current values of the Y vector and time T and put them into the vector D. For a single equation only Y(l) and D(1) are used. The step size H and the number NS of steps are selected by the user. 

CALL Functamax, Fmax) User supplied subroutine CALL Func (amin, Fmin)... 

The computational scheme presented here can be used for any reaction scheme with only a user-supplied subroutine for the kinetic rate form for the various reactions and the physico-chemical parameters of the system. It can also be used as rate... 

FE analysis using an advanced material model for polymers Can account for complex geometries Can account for the experimentally determined characteristic response Enables simulations of complex thermomechanical, composite responses The advanced material models are currentiy only available as user-supplied subroutines for the FE packages Requires expertise both to calibrate and use... 

Advanced material models are currently only available as user-supplied subroutines for finite element packages Requires expertise both to calibrate and use... 

The difference between using a user-supplied subroutine and one of the built-in functions is the need to compile the subroutine. Figure 9.6 demonstrates how this is done. Instead of going to Aspen User Interface, you go to Aspen Simulation Engine and use the DOS-like command aspcomp ramtbe.f to compile the subroutine. Of course, you need to have a Fortran compiler on your computer. Figure 9.7 lists the RAMTBE.f Fortran program in which the chemical equilibrium constant, activities, and reaction rates are calculated. 

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