Material Modelling and Fundamental Solutions - The Boundary Element Method with Programming - page 72

Equation (4.16) can also be rewritten as

cos T

(4.19)

T P , Q

2 r

S

where

1

^ ` ^ `

cos T n x r with n n ,n and r r ,r

(4.20)

x y x y

r

Subroutines for the isotropic solutions are presented below.

MODULE Laplace_lib
REAL :: PI=3.14159265359
CONTAINS
REAL FUNCTION U(r,k,Cdim)
! Fundamental solution for Potential problems
! Temperature/Potential isotropic material
REAL,INTENT(IN) :: r ! Distance source and field point
REAL,INTENT(IN) :: k ! Conducivity
INTEGER,INTENT(IN) :: Cdim ! Cartesian dimension (2-D,3-D)
SELECT CASE (CDIM)
CASE (2) ! Two-dimensional solution
U= 1.0/(2.0*Pi*k)*LOG(1/r)
CASE (3) ! Three-dimensional solution
U= 1.0/(4.0*Pi*r*k)
CASE DEFAULT
U=0.0
WRITE (11,*)'Cdim not equal 2 or 3 in Function U(...)'
END SELECT
END FUNCTION U
REAL FUNCTION T(r,dxr,Vnorm,Cdim)
! Fundamental solution for Potential problems
! Flow, isotropic material
REAL,INTENT(IN):: r ! Distance source and field point
REAL,INTENT(IN):: dxr(:) ! r ,x ,r ,y ,r ,z
REAL,INTENT(IN):: Vnorm(:) ! Normal vector
INTEGER,INTENT(IN) :: Cdim ! Cartesian dimension
SELECT CASE (Cdim)
CASE (2) ! Two-dimensional solution
T= DOT_PRODUCT (Vnorm,dxr)/(2.0*Pi*r)
CASE (3) ! Three-dimensional solution
T= DOT_PRODUCT (Vnorm,dxr)/(4.0*Pi*r*r)
CASE DEFAULT
T=0.0
WRITE (11,*)'Cdim not equal 2 or 3 in Function T(...)'
END SELECT
END FUNCTION T
END MODULE Laplace_lib