Multiple regions - The Boundary Element Method with Programming - page 305

For the treatment of the individual regions we have to renumber the
nodes/degrees of freedom for each region into a local (region) numbering
system, as explained previously. The incidence and destination vectors of
boundary elements, as well as coordinate vector, are modified accordingly.

b. Determine K and A and results due to “fixed” interface nodes

The next task is to determine matrix K . At the same time we assemble it into
the global system of equations using the interface destination vector. For
partially coupled problems, we calculate and store, at the same time, the results
for the elements due to zero values of ^` u at the interface. These values are
stored in the element result vectors Elres_u and Elres_t. Matrix A and the
vector {t } c are also determined and stored.

3. Solve global system of equations

The global system of equations is solved for the interface unknowns ^` c

u

For each region determine ^` c

t and ^` u
Using equation (11.27) the values for the fluxes/tractions at the interface and (for
partially coupled problems) the temperatures/displacements at the free nodes are
determined and added to the values already stored in Elres_u and Elres_t. Note that
before Equation (11.27) can be used the interface unknowns have to be gathered
from the interface vector using the relationship between interface and region
numbering in Table 11.3.

4.

PROGRAM General_purpose_MRBEM
!------------------------------------------------
! General purpose BEM program
! for solving elasticity and potential problems
! with multiple regions
!------------------------------------------------------
USE Utility_lib; USE Elast_lib; USE Laplace_lib
USE Integration_lib; USE Stiffness_lib
IMPLICIT NONE
INTEGER, ALLOCATABLE :: NCode(:,:) ! Element BC´s
INTEGER, ALLOCATABLE :: Ldest_KBE(:) ! Interface destinations
INTEGER, ALLOCATABLE :: TypeR(:) ! Type of BE-regions
REAL, ALLOCATABLE :: Elcor(:,:) ! Element coordinates
REAL, ALLOCATABLE :: xP(:,:) ! Node co-ordinates
REAL, ALLOCATABLE :: Elres_u(:,:) ! Element results
REAL, ALLOCATABLE :: Elres_t(:,:) ! Element results
REAL(KIND=8), ALLOCATABLE :: KBE(:,:,:) ! Region stiffness
REAL(KIND=8), ALLOCATABLE :: A(:,:,:) ! Results due to ui=1
REAL(KIND=8), ALLOCATABLE :: Lhs(:,:),Rhs(:) ! global matrices