C*************************************************************** C Test program for subroutine RIM3 by Stephen Kirkup C*************************************************************** C C Copyright 2004- Stephen Kirkup C School of Computing Engineering and Physical Sciences C University of Central Lancashire - www.uclan.ac.uk C smkirkup@uclan.ac.uk C http://www.researchgate.net/profile/Stephen_Kirkup C C This open source code can be found at C www.boundary-element-method.com/fortran/RIM3T2.FOR C C Issued under the GNU General Public License 2007, see gpl.txt C C Part of the the author's open source BEM packages. C All codes and manuals can be downloaded from C www.boundary-element-method.com C C*************************************************************** C C This program is a test for the subroutine RIM3. The program computes C the solution to an acoustic/Helmholtz problem exterior to a square C plate lying in a rigid baffle. C C Background C ---------- C C The Helmholtz problem arises when harmonic solutions of the wave C equation C 2 C __ 2 1 d {\Psi}(p,t) C \/ {\Psi}(p,t) - ---- --------------- = 0 C 2 2 C c d t C C are sought, where {\Psi}(p,t) is the scalar time-dependent velocity C potential. In the cases where {\Psi} is periodic, it may be C approximated as a set of frequency components that may be analysed C independently. For each frequency a component of the form C C {\phi}(p) exp(i {\omega} t) C C (where {\omega} = 2 * {\pi} * frequency) the wave equation can be C reduced to the Helmholtz equation C C __ 2 2 C \/ {\phi} + k {\phi} = 0 C C where k (the wavenumber) = {\omega}/c (c=speed of sound in the C medium. {\phi} is known as the velocity potential. C C For the exterior problem, the domain lies exterior to a closed C plate \Pi. The plate condition may be Dirichlet, Robin or C Neumann. It is assumed to have the following general form C C {\alpha}(q) {\phi}(q) + {\beta}(q) v(q) = f(q) C C where {\phi}(q) is the velocity potential at the point q on \Pi, v(q) C is the derivative of {\phi} with respect to the outward normal to \Pi C at q and {\alpha}, {\beta} and f are complex-values functions defined C on \Pi. C C Subroutine RIM3 accepts the wavenumber, a description of the C plate of the domain and the position of the exterior points C where the solution ({\phi}) is sought, the plate condition and C returns the solution ({\phi} and v) on \Pi and the value of {\phi} C at the exterior points. C C The test problems C ----------------- C C In this test the domain is a square plate with side of length 1m C lying in an infinite rigid baffle. The acoustic medium is air (at 20 C celcius and 1 atmosphere, c=344.0 (metres per second), density C {\rho}=1.205 (kilograms per cubic metre) and the solution to the C problem with a Neumann plate condition v=1 (that is \alpha=1, \beta=0, C f=1). C The plate is described by a set of NPI=32 planar triangular elements C of equal size. The radiation ratio is computed for a range of C frequencies. C---------------------------------------------------------------------- C The PARAMETER statement C ----------------------- C There are four components in the PARAMETER statement. C integer MAXNS : The limit on the number of plate elements. C integer MAXNV : The limit on the number of vertices. C integer MAXNFR : The limit on the number of frequencies. C integer MAXNPE : The limit on the number of exterior points. C External modules related to the package C --------------------------------------- C subroutine RIM3: Subroutine for solving the exterior Helmholtz C equation (file EBEM2.FOR contains EBEM2 and subordinate routines) C subroutine H3LC: Returns the individual discrete Helmholtz integral C operators. (file H3LC.FOR contains H3LC and subordinate routines) C subroutine CGLS: Solves a general linear system of equations. C (file CGLS.FOR contains CGSL and subordinate routines) C file GEOM3D.FOR contains the set of relevant geometric subroutines C The program PROGRAM RIM3T IMPLICIT NONE C VARIABLE DECLARATION C -------------------- C PARAMETERs for storing the limits on the dimension of arrays C Limit on the number of elements INTEGER MAXNPI PARAMETER (MAXNPI=40) C Limit on the number of vertices (equal to the number of elements) INTEGER MAXNV PARAMETER (MAXNV=40) C Limit on the number of points exterior to the plate, where C acoustic properties are sought INTEGER MAXNPE PARAMETER (MAXNPE=6) C Constants C Real scalars: 0, 1, 2, pi REAL*8 ZERO,ONE,TWO,THREE,FOUR,PI C Complex scalars: (0,0), (1,0), (0,1) COMPLEX*16 CZERO,CONE,CIMAG C Properties of the acoustic medium C The speed of sound [standard unit: metres per second] REAL*8 CVAL C The density [standard unit: kilograms per cubic metre] REAL*8 RHOVAL C Wavenumber parameter for RIM3 REAL*8 K C Angular frequency COMPLEX*16 OMEGA C Geometrical description of the plate(ies) C Number of elements and counter INTEGER NPI,IPI C Number of collocation points (on \Pi) and counter INTEGER NPIP,ISP C Number of vetices and counter INTEGER NV,IV C Index of nodal coordinate for defining boundaries (standard unit is C metres) REAL*8 VERTEX(MAXNV,3) C The three nodes that define each element on the boundaries INTEGER PIELV(MAXNPI,3) C The points exterior to the plate(ies) where the acoustic C properties are sought and the directional vectors at those points. C [Only necessary if an exterior solution is sought.] C Number of exterior points INTEGER NPE C Coordinates of the exterior points REAL*8 PEXT(MAXNPE,3) C Data structures that contain the parameters that define the test C problems C The acoustic frequency for each test. FRVAL is assigned the C acoustic frequency of the i-th test problem. REAL*8 FRVAL C Data structures that are used to define each test problem in turn C and are input parameters to RIM3. C PIALPHA(j) is assigned the value of {\alpha} at the centre of the C j-th element. COMPLEX*16 PIALPHA(MAXNPI) C PIBETA(j) is assigned the value of {\beta} at the centre of the C j-th element. COMPLEX*16 PIBETA(MAXNPI) C PIF(j) is assigned the value of f at the centre of the j-th element. COMPLEX*16 PIF(MAXNPI) C Validation and control parameters for RIM3 C Switch for particular solution LOGICAL LSOL C Validation switch LOGICAL LVALID C The maximum absolute error in the parameters that describe the C geometry of the plate. REAL*8 EGEOM C Output from subroutine RIM3 C The velocity potential (phi - the solution) at the centres of the C elements COMPLEX*16 PIPHI(MAXNPI) C The normal derivative of the velocity potential at the centres of the C elements COMPLEX*16 PIV(MAXNPI) C The velocity potential (phi - the solution) at exterior points COMPLEX*16 PEPHI(MAXNPE) C Workspace for RIM3 COMPLEX*16 WKSPC1(MAXNPI,MAXNPI) COMPLEX*16 WKSPC2(MAXNPE,MAXNPI) COMPLEX*16 WKSPC3(MAXNPI,MAXNPI) COMPLEX*16 WKSPC4(MAXNPI) COMPLEX*16 WKSPC5(MAXNPI) LOGICAL WKSPC6(MAXNPI) C Acoustic properties. These data structures are appended after each C execution of RIM3 and contain the numerical solution to the test C problems. C Sound intensity [standard unit: watts per square metre] REAL*8 PIINTY(MAXNPI) REAL*8 POWER,BAFFPOW C Counter through the x,y coordinates INTEGER ICOORD C Local storage of pressure, pressure/velocity COMPLEX*16 PRESSURE C The coordinates of the centres of the elements REAL*8 SELCNT(MAXNPI,3) REAL*8 EPS C Number of test problems (wavenumbers) and counter INTEGER NTEST,ITEST C INITIALISATION C -------------- C Set constants ZERO=0.0D0 ONE=1.0D0 TWO=2.0D0 THREE=3.0D0 FOUR=4.0D0 PI=4.0D0*ATAN(ONE) CZERO=CMPLX(ZERO,ZERO) CONE=CMPLX(ONE,ZERO) CIMAG=CMPLX(ZERO,ONE) EPS=1.0E-10 C Describe the nodes and elements that make up the plate C :The square is divided into NPI=32 uniform elements. VERTEX and C : PIELV are defined anti-clockwise around the plate so that the C : normal to the plate is assumed to be outward C :Set up nodes C : Set NPI, the number of elements NPI=32 C : Set NV, the number of vertices (equal to the number of elements) NV=25 C : Set up VERTEX, the coordinates of the vertices of the elements NV=25 DATA ((VERTEX(IV,ICOORD),ICOORD=1,3),IV=1,25) * / 0.000D0, 0.000D0, 0.000D0, * 0.250D0, 0.000D0, 0.000D0, * 0.500D0, 0.000D0, 0.000D0, * 0.750D0, 0.000D0, 0.000D0, * 1.000D0, 0.000D0, 0.000D0, * 0.000D0, 0.250D0, 0.000D0, * 0.250D0, 0.250D0, 0.000D0, * 0.500D0, 0.250D0, 0.000D0, * 0.750D0, 0.250D0, 0.000D0, * 1.000D0, 0.250D0, 0.000D0, * 0.000D0, 0.500D0, 0.000D0, * 0.250D0, 0.500D0, 0.000D0, * 0.500D0, 0.500D0, 0.000D0, * 0.750D0, 0.500D0, 0.000D0, * 1.000D0, 0.500D0, 0.000D0, * 0.000D0, 0.750D0, 0.000D0, * 0.250D0, 0.750D0, 0.000D0, * 0.500D0, 0.750D0, 0.000D0, * 0.750D0, 0.750D0, 0.000D0, * 1.000D0, 0.750D0, 0.000D0, * 0.000D0, 1.000D0, 0.000D0, * 0.250D0, 1.000D0, 0.000D0, * 0.500D0, 1.000D0, 0.000D0, * 0.750D0, 1.000D0, 0.000D0, * 1.000D0, 1.000D0, 0.000D0/ C : Set nodal indices that describe the elements of the plate. C : The indices refer to the nodes in VERTEX. The order of the C : nodes in PIELV dictates that the normal is outward from the C : plate into the acoustic domain. DATA ((PIELV(IPI,ICOORD),ICOORD=1,3),IPI=1,32) * / 1, 2, 6, 2, 7, 6, 2, 3, 8, 2, 8, 7, * 3, 4, 8, 4, 9, 8, 4, 5,10, 4,10, 9, * 6, 7,12, 6,12,11, 7, 8,12, 8,13,12, * 8, 9,14, 8,14,13, 9,10,14, 10,15,14, * 11,12,16, 12,17,16, 12,13,18, 12,18,17, * 13,14,18, 14,19,18, 14,15,20, 14,20,19, * 16,17,22, 16,22,21, 17,18,22, 18,23,22, * 18,19,24, 18,24,23, 19,20,24, 20,25,24/ C Set the centres of the elements, the collocation points DO 100 IPI=1,NPI SELCNT(IPI,1)=(VERTEX(PIELV(IPI,1),1) * +VERTEX(PIELV(IPI,2),1)+VERTEX(PIELV(IPI,3),1))/THREE SELCNT(IPI,2)=(VERTEX(PIELV(IPI,1),2) * +VERTEX(PIELV(IPI,2),2)+VERTEX(PIELV(IPI,3),2))/THREE SELCNT(IPI,3)=(VERTEX(PIELV(IPI,1),3) * +VERTEX(PIELV(IPI,2),3)+VERTEX(PIELV(IPI,3),3))/THREE 100 CONTINUE C Set NPE=1 NPE=1 PEXT(1,1)=0.5D0 PEXT(1,2)=0.5D0 PEXT(1,3)=0.1D0 C The number of points on the plate is equal to the number of C elements NPIP=NPI C Set up test problems C :Set the number of test problems NTEST=100 C Properties of the acoustic medium. C the propagation velocity C and RHO the density of the acoustic medium. C>0, RHO>0 C :Acoustic medium is air at 20 celcius and 1 atmosphere. C [C in metres per second, RHO in kilograms per cubic metre.] CVAL=344.0D0 RHOVAL=1.205D0 C Open file for the output data OPEN(UNIT=20,FILE='RIM3T2.OUT') DO 200 ITEST=1,NTEST C :Set acoustic frequency value (hertz) in FRVAL FRVAL=10.0D0*DFLOAT(ITEST) C : Set the wavenumber in K K=TWO*PI*FRVAL/CVAL C Set up particular alpha and beta functions for this wavenumber C and type of plate condition DO 310 ISP=1,NPIP PIALPHA(ISP)=CZERO PIBETA(ISP)=CONE PIF(ISP)=CONE 310 CONTINUE C :Switch for particular solution LSOL=.TRUE. C :Switch on the validation of RIM3 LVALID=.TRUE. C :Set EGEOM EGEOM=1.0D-6 C Set OMEGA, the angular frequency omega and K, the wavenumber OMEGA=2.0D0*PI*FRVAL C Call RIM3 CALL RIM3(K, * MAXNV,NV,VERTEX,MAXNPI,NPI,PIELV, * MAXNPE,NPE,PEXT, * PIALPHA,PIBETA,PIF, * LSOL,LVALID,EGEOM, * PIPHI,PIV,PEPHI, * WKSPC1,WKSPC2,WKSPC3,WKSPC4,WKSPC5,WKSPC6) C Compute the pressure and the intensity at points on the plate DO 400 ISP=1,NPIP PRESSURE=CIMAG*RHOVAL*OMEGA*PIPHI(ISP) PIINTY(ISP)=DBLE(CONJG(PRESSURE)*PIV(ISP))/TWO 400 CONTINUE C Compute the power and radiation ratio POWER=0.0D0 BAFFPOW=0.0D0 DO 695 ISP=1,NPIP POWER=POWER+PIINTY(ISP) BAFFPOW=BAFFPOW+RHOVAL*CVAL*ABS(CONJG(PIV(ISP))*PIV(ISP))/TWO 695 CONTINUE C Output the radiation ratio WRITE(20,*) K,POWER/BAFFPOW C Close loop(ITEST) through the test problems 200 CONTINUE CLOSE(20) END