Subroutine ledhmz2

subroutine ledhmz2

        ! Variables
    integer, intent(in) :: n1
    integer, intent(in) :: m1
    integer, intent(in) :: nf
    integer, intent(in) :: nu
    integer, intent(in) :: flag1
    integer, intent(in) :: flag2
    integer, intent(in) :: fdim1
    integer, intent(in) :: fdim2
    integer, intent(in) :: init
    double precision, intent(in) :: rm
    double precision, intent(in) :: beta
    double precision, intent(in), dimension (fdim1,fdim1) :: e1
    double precision, intent(in), dimension (fdim1-flag1,fdim1-flag1) :: e2
    double precision, intent(in), dimension (fdim1) :: w1
    double precision, intent(in), dimension (fdim1-flag1) :: w2
    double precision, intent(inout), dimension (0:nf,0:m1) :: f
    double precision, intent(inout), dimension (0:nu,0:m1) :: u
    integer :: i
    integer :: j
    integer :: m
    integer :: n
    double precision, dimension (fdim1,fdim2) :: f1
    double precision, dimension (fdim1-flag1,fdim2) :: f2
    double precision, dimension (fdim1,fdim2-flag2) :: f3
    double precision, dimension (fdim1-flag1,fdim2-flag2) :: f4
    double precision, dimension (fdim1,fdim2) :: ftmp1
    double precision, dimension (fdim1-flag1,fdim2) :: ftmp2
    double precision, dimension (fdim1,fdim2-flag2) :: ftmp3
    double precision, dimension (fdim1-flag1,fdim2-flag2) :: ftmp4
    double precision :: val
    double precision :: rm1
    double precision :: rm2

end subroutine ledhmz2

subroutine ledhmz2(n1,m1,rm,beta,f,nf,u,nu,e1,e2,w1,w2,init,flag1,flag2,fdim1,fdim2)

Solve the 2D Helmholtz equation: rm*u - u_xx - beta u_yy= f with homogeneous Dirichlet B.C. in IxI.

Input:

f: f(0:nf, 0:m1) coefficients in Legendre of right hand side f
nf: nf>=n1
e,w: Output from ledeig.f, contain eigenfunctions and eigenvalues of -u_{xx}= \lambda u.
ws: working array. There are initialized with init=1, they can be repeatedly used with init.ne.1.
rm,beta: constants in the Helmholtz equation
init: initialization flag: init=1, initialize ws.

Output:

u, coefficients in Legendre of the solution. (nu >= n1)

This routine is a internal part of the specpack package, but can be used directly if one is content with the input and output in spectral space. For more documentation regarding the use of the SpecPack package: see the package documentation.

Author: Jan Ivar Moldekleiv, Jie Shen

Version: 0.8

Description of Variables

n1

integer, intent(in) :: n1

Leading dimension of rh.side

m1

integer, intent(in) :: m1

Second dimension of rh. side

nf

integer, intent(in) :: nf

Leading dim. of array containing rh. side. nf >= n1

nu

integer, intent(in) :: nu

Leading dim. of array containing solution. nu >= n1

flag1

integer, intent(in) :: flag1

Determines the dimension of e1 & e2

flag2

integer, intent(in) :: flag2

Determines the dimension of e1 & e2

fdim1

integer, intent(in) :: fdim1

Determines the dimension of e1 & e2

fdim2

integer, intent(in) :: fdim2

Determines the dimension of e1 & e2

init

integer, intent(in) :: init

initialization flag: init=1, initialize ws

rm

double precision, intent(in) :: rm

The constant rm in the helmholtz equation.

beta

double precision, intent(in) :: beta

The constant beta in the helmholtz equation.

e1

double precision, intent(in), dimension (fdim1,fdim1) :: e1

First part of eigenfunctions from ledeig.

e2

double precision, intent(in), dimension (fdim1-flag1,fdim1-flag1) :: e2

Second part of eigenfunctions.

w1

double precision, intent(in), dimension (fdim1) :: w1

Eigenvalues from ledeig.

w2

double precision, intent(in), dimension (fdim1-flag1) :: w2

Second part of eigenvalues from ledeig.

f

double precision, intent(inout), dimension (0:nf,0:m1) :: f

The righthandside after letrfm2

u

double precision, intent(inout), dimension (0:nu,0:m1) :: u

The solution before letrfm2

i

integer :: i

Local variable

j

integer :: j

Local variable

m

integer :: m

Local variable

n

integer :: n

Local variable

f1

double precision, dimension (fdim1,fdim2) :: f1

Local variable

f2

double precision, dimension (fdim1-flag1,fdim2) :: f2

Local variable

f3

double precision, dimension (fdim1,fdim2-flag2) :: f3

Local variable

f4

double precision, dimension (fdim1-flag1,fdim2-flag2) :: f4

Local variable

ftmp1

double precision, dimension (fdim1,fdim2) :: ftmp1

Local variable

ftmp2

double precision, dimension (fdim1-flag1,fdim2) :: ftmp2

Local variable

ftmp3

double precision, dimension (fdim1,fdim2-flag2) :: ftmp3

Local variable

ftmp4

double precision, dimension (fdim1-flag1,fdim2-flag2) :: ftmp4

Local variable

val

double precision :: val

Local variable

rm1

double precision :: rm1

Local variable

rm2

double precision :: rm2

Local variable