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SEMICON1.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME SEMICON1
* Problem :
* *********
* The semiconductor problem by Rheinboldt, using a finite difference
* approximation.
* Source: problem 10 in
* J.J. More',
* "A collection of nonlinear model problems"
* Proceedings of the AMS-SIAM Summer seminar on the Computational
* Solution of Nonlinear Systems of Equations, Colorado, 1988.
* Argonne National Laboratory MCS-P60-0289, 1989.
* SIF input: Ph. Toint, Dec 1989.
* classification NOR2-AN-V-V
* N = Number of discretized point inside the interval [a, b]
* LN = Index of the last negative discretization point
* (the interest is in the negative part)
IE N 10 $-PARAMETER original value
IE LN 9 $-PARAMETER original value
*IE N 50 $-PARAMETER
*IE LN 45 $-PARAMETER
*IE N 100 $-PARAMETER
*IE LN 90 $-PARAMETER
*IE N 500 $-PARAMETER
*IE LN 450 $-PARAMETER
*IE N 1000 $-PARAMETER
*IE LN 900 $-PARAMETER
IE N 5000 $-PARAMETER
IE LN 4500 $-PARAMETER
* Continuation parameter
* Interesting values: 0.0 (the solution is a straight line)
* 0.2
* 1.0 (the true semiconductor equation)
RE LAMBDA 1.0 $-PARAMETER continuation parameter
* The bounds of the interval [a, b] = [ X(0), X(N+1)] which should
* contain zero
RE A -0.00009
RE B 0.00001
* Boundary values
RE UA 0.0
RE UB 700.0
* Problem's constants
RE CA 1.0D12
RE CB 1.0D13
RE BETA 40.0
* Other parameter definitions
IA LN+1 LN 1
IA N+1 N 1
RM -A A -1.0
R+ B-A B -A
RI RN+1 N+1
RD TMP RN+1 1.0
R* H B-A TMP
R* H2 H H
R* LB LAMBDA BETA
R* H2CA H2 CA
R* H2CB H2 CB
R* LH2CA LAMBDA H2CA
R* LH2CB LAMBDA H2CB
R* LUA LAMBDA UA
R* LUB LAMBDA UB
RA ULW LUA -5.0
RA UUP LUB 5.0
RM -LB LB -1.0
RM -LUB LUB -1.0
RM -LH2CB LH2CB -1.0
* Constants
IE 0 0
IE 1 1
VARIABLES
DO I 0 N+1
X U(I)
ND
GROUPS
DO I 1 N
IA I+1 I 1
IA I-1 I -1
XE G(I) U(I-1) 1.0
XE G(I) U(I) -2.0
XE G(I) U(I+1) 1.0
ND
CONSTANTS
DO I 1 LN
Z SEMICON1 G(I) LH2CA
ND
DO I LN+1 N
Z SEMICON1 G(I) -LH2CB
ND
BOUNDS
ZU SEMICON1 'DEFAULT' UUP
ZL SEMICON1 'DEFAULT' ULW
* Fix the boundary conditions
ZX SEMICON1 U(0) LUA
ZX SEMICON1 U(N+1) LUB
START POINT
XV SEMICON1 'DEFAULT' 0.0
ZV SEMICON1 U(0) LUA
ZV SEMICON1 U(N+1) LUB
ELEMENT TYPE
EV WE1 X
EP WE1 LAC LAB
EP WE1 LU
ELEMENT USES
DO I 1 N
XT EA(I) WE1
ZV EA(I) X U(I)
ZP EA(I) LAC LH2CA
ZP EA(I) LAB -LB
ZP EA(I) LU LUA
XT EB(I) WE1
ZV EB(I) X U(I)
ZP EB(I) LAC -LH2CB
ZP EB(I) LAB LB
ZP EB(I) LU LUB
ND
GROUP USES
DO I 1 N
XE G(I) EA(I) EB(I)
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS SEMICON1
TEMPORARIES
R FVAL
M EXP
INDIVIDUALS
T WE1
A FVAL LAC * EXP( LAB * ( X - LU ) )
F FVAL
G X LAB * FVAL
H X X LAB * LAB * FVAL
ENDATA