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PROCEDURE mtt_update(VAR xnew : StateVector;
dx,x : StateVector;
DT : REAL;
Nx : INTEGER;
METHOD : IntegrationMethod;
VAR A : StateMatrix);
CONST
Small = 0.000001;
VAR
i,j : INTEGER;
AA : StateMatrix;
ELSE IF (Method=2) OR (METHOD=3) THEN {Implicit}
BEGIN
{Set up the solution matrices:
AA = eye(Nx)-A*dt
BB = x + dt*(dx - A*x)}
FOR i := 1 TO Nx DO
BEGIN
Ax[i] := 0.0;
FOR j := 1 TO Nx DO
BEGIN
AA[i,j] := -A[i,j]*DT;
Ax[i] := Ax[i] + A[i,j]*x[j];
IF i=j THEN
AA[i,j] := AA[i,j] + 1.0;
END
END;
FOR i := 1 TO Nx DO
BB[i] := x[i] + DT*(dx[i]-Ax[i]);
{Solve the equation AAx = B}
mtt_solve(xnew,AA,BB,Nx,Small);
END
ELSE IF (METHOD=4) THEN {Sparse CG implicit}
BEGIN
mtt_asub(x,Ax,Nx); {Sparse computation of (1-A*dt)*x}
FOR i := 1 TO Nx DO
BB[i] := Ax[i]+ DT*dx[i];
mtt_sparse(BB,Nx,xnew,rsq); {Sparse CG solution
- using prev. xnew as starter}
END
ELSE
Writeln("Method >4 is not defined");
END{mtt_update};
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PROCEDURE mtt_update(VAR xnew : StateVector;
dx,x : StateVector;
DT : REAL;
Nx : INTEGER;
METHOD : IntegrationMethod;
AA : StateMatrix );
{
###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
###############################################################
}
CONST
Small = 0.000001;
VAR
i,j : INTEGER;
BB,Ax : StateVector;
rsq : REAL;
(*$I mtt_solve.p *)
(*$I mtt_sparse.p *)
BEGIN{mtt_update}
IF Method=1 THEN {Euler}
FOR i := 1 TO Nx DO
xnew[i] := xnew[i] + dx[i]*DT
ELSE IF (Method=2) OR (METHOD=3) OR (METHOD=4) THEN {Implicit}
BEGIN {Implicit methods}
mtt_asub(x,Ax,Nx); {Sparse computation of (1-A*dt)*x}
FOR i := 1 TO Nx DO {BB is (1-A*dt)*x +dx*dt}
BB[i] := Ax[i]+ DT*dx[i];
{Solve the equation AAx = B}
IF (Method=2) OR (METHOD=3) THEN {Use SVD}
mtt_solve(xnew,AA,BB,Nx,Small)
ELSE {Sparse CG solution}
mtt_sparse(BB,Nx,xnew,rsq);
END{Implicit methods}
ELSE
Writeln("Method >4 is not defined");
END{mtt_update};
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