C\$TEST DTTGU5 c main program5 common /cstak/ ds double precision ds(350000) external handlu, bc, af integer ndx, ndy, istkgt, is(1000), iu, ix, temp, temp1 integer nu, nr, iyb(5), ixb(5), kx, ky integer nxr(5), nyr(5), kxr(5), kyr(5) integer idumb real errpar(2), rs(1000) logical ls(1000) complex cs(500) double precision tstart, dt, rx double precision ws(500), tstop equivalence (ds(1), cs(1), ws(1), rs(1), is(1), ls(1)) c to solve laplaces equation with real ( z*log(z) ) as solution. c the port library stack and its aliases. c initialize the port library stack length. call istkin(350000, 4) call enter(1) nu = 1 kx = 4 ky = 4 ndx = 3 ndy = 3 nr = 5 tstart = 0 dt = 1.d0 tstop =1.d0 errpar(1) = 1e-2 errpar(2) = 1e-4 nx = ndx+2*(kx-1) rx=1.0d0 c space for x mesh for rectangle 1 ix = istkgt(nx, 4) c 0 and rx mult = kx. ixb(1)=ix do 1 i = 1, kx temp = ix+i ws(temp-1) = 0 temp = ix+nx-i ws(temp) = rx 1 continue temp = ndx-1 do 2 i = 1, temp temp1 = ix+kx-2+i ws(temp1) = rx*(dble(float(i-1))/(dble(float(ndx))-1d0))**kx 2 continue c rectangle 2 has same grid in x direction as rectanlge 1 ixb(2)=istkgt(nx, 4) call dcopy(nx, ws(ix), 1, ws(ixb(2)), 1) c uniform grid for rectanlges 3,4, and 5 in x direction ixb(3) = idumb(1.0d0, 2.0d0, ndx, kx, nxr(3)) ixb(4) = idumb(2.0d0, 3.0d0, ndx, kx, nxr(4)) ixb(5) = idumb(2.0d0, 3.0d0, ndx, kx, nxr(5)) ny = ndy+2*(ky-1) c rectangles 1,3, and 4 use the same grid in the y direction as c is used for the x direction in rectangle 1 c space for y mesh. iyb(1) = istkgt(ny, 4) call dcopy( nx, ws(ix), 1, ws(iyb(1)), 1) iyb(3) =istkgt(ny, 4) call dcopy( nx, ws(ix), 1, ws(iyb(3)), 1) iyb(4) =istkgt(ny, 4) call dcopy( nx, ws(ix), 1, ws(iyb(4)), 1) c rectangles 2 and 5 use uniform mesh in y direction iyb(2) = idumb(1.0d0, 2.0d0, ndy, ky, nyr(2)) iyb(5) = idumb(1.0d0, 2.0d0, ndy, ky, nyr(5)) c space for the solution. nnu=0 do 3 i=1,nr nxr(i)=nx nyr(i)=ny nnu=nnu+nu*((nxr(i)-kx)*(nyr(i)-ky)) 3 continue iu = istkgt(nnu, 4) do 4 i=1,nr kxr(i)=kx kyr(i)=ky 4 continue call setd(nnu, 0.0d0,ws(iu)) call dttgu(ws(iu),nu,nr,kxr,ws,nxr,ixb,kyr,ws,nyr,iyb,tstart, 1 tstop, dt, af, bc, errpar, handlu) call leave call wrapup stop end subroutine af(t, xi, nx, yi, ny, nu, u, ut, ux, uy, uxt, 1 uyt, a, au, aut, aux, auy, auxt, auyt, f, fu, fut, fux, fuy, 2 fuxt, fuyt) integer nu, nx, ny double precision t, xi(nx), yi(ny), u(nx, ny, nu), ut(nx, ny, nu), 1 ux(nx, ny, nu) double precision uy(nx, ny, nu), uxt(nx, ny, nu), uyt(nx, ny, nu), 1 a(nx, ny, nu, 2), au(nx, ny, nu, nu, 2), aut(nx, ny, nu, nu, 2) double precision aux(nx, ny, nu, nu, 2), auy(nx, ny, nu, nu, 2), 1 auxt(nx, ny, nu, nu, 2), auyt(nx, ny, nu, nu, 2), f(nx, ny, nu) 2 , fu(nx, ny, nu, nu) double precision fut(nx, ny, nu, nu), fux(nx, ny, nu, nu), fuy(nx, 1 ny, nu, nu), fuxt(nx, ny, nu, nu), fuyt(nx, ny, nu, nu) integer i, p, q do 3 i = 1, nu do 2 q = 1, ny do 1 p = 1, nx a(p, q, i, 1) = ux(p, q, i) a(p, q, i, 2) = uy(p, q, i) aux(p, q, i, i, 1) = 1 auy(p, q, i, i, 2) = 1 1 continue 2 continue 3 continue return end subroutine bc(t, x, nx, y, ny, lx, rx, ly, ry, u, ut, ux, 1 uy, uxt, uyt, nu, b, bu, but, bux, buy, buxt, buyt) integer nu, nx, ny double precision t, x(nx), y(ny), lx, rx, ly double precision ry, u(nx, ny, nu), ut(nx, ny, nu), ux(nx, ny, nu) 1 , uy(nx, ny, nu), uxt(nx, ny, nu) double precision uyt(nx, ny, nu), b(nx, ny, nu), bu(nx, ny, nu, 1 nu), but(nx, ny, nu, nu), bux(nx, ny, nu, nu), buy(nx, ny, nu 2 , nu) double precision buxt(nx, ny, nu, nu), buyt(nx, ny, nu, nu) integer i, j double precision r, dcos, dlog, dsin, datan, theta double precision dsqrt do 6 j = 1, ny do 5 i = 1, nx if (y(j) .ne. ly) goto 1 b(i, j, 1) = uy(i, j, 1) c neumann data on bottom. buy(i, j, 1, 1) = 1 goto 4 1 r = dsqrt(x(i)**2+y(j)**2) c dirichlet data. if (x(i) .le. 0d0) goto 2 theta = datan(y(j)/x(i)) goto 3 2 theta = 2d0*datan(1d0) 3 b(i, j, 1) = u(i, j, 1)-r*(dcos(theta)*dlog(r)-theta* 1 dsin(theta)) bu(i, j, 1, 1) = 1 4 continue 5 continue 6 continue return end subroutine ewe2(t, x, nx, y, ny, u, inu, ir) integer inu,ir, nx, ny double precision t, x(nx), y(ny), u(nx, ny) integer i, j double precision r, dcos, dlog, dsin, datan, theta double precision dsqrt c the exact solution. do 6 i = 1, nx do 5 j = 1, ny r = dsqrt(x(i)**2+y(j)**2) if (x(i) .le. 0d0) goto 1 theta = datan(y(j)/x(i)) goto 2 1 theta = 2d0*datan(1d0) 2 if (r .le. 0d0) goto 3 u(i, j) = r*(dcos(theta)*dlog(r)-theta*dsin(theta)) goto 4 3 u(i, j) = 0 4 continue 5 continue 6 continue return end subroutine handlu(t0, u0, t, u, nv, dt, tstop) integer nv double precision t0, u0(nv), t, u(nv), dt, tstop common /d7tgup/ errpar, nu, mxp, myp integer nu real errpar(2) common /d7tgum/ kxp,ix,nxp,kyp,iy,nyp,nxnyt,nr,iup integer kx, ix, nx, ky, iy, ny common /cstak/is integer is(1000) iwrite=i1mach(2) if (t0 .ne. t) goto 2 write (iwrite, 1) t 1 format (16h restart for t =, 1pe10.2) return c get and print the error. 2 continue write(iwrite, 3)t 3 format(6h at t=,1pe10.2) ius=1 do 5 inu = 1, nu iyr=iy ixr=ix do 4 ir=1,nr ir1=ir-1 nx=is(nxp+ir1) ny=is(nyp+ir1) kx=is(kxp+ir1) ky=is(kyp+ir1) call gerr(kx, ixr, nx, ky, iyr, ny, u(ius), inu, t, ir) ixr=ixr+nx iyr=iyr+ny ius=ius+(nx-kx)*(ny-ky) 4 continue 5 continue return end subroutine gerr(kx, ix, nx, ky, iy, ny, u, inu, t, ir) integer kx, ix, nx, ky, iy, ny, inu, ir double precision u(1), t common /cstak/ ds double precision ds(500) integer ifa, ita(2), ixa(2), nta(2), nxa(2), idlumd integer ixs, iys, nxs, nys, istkgt, i integer iewe, ka(2), ma(2), is(1000), i1mach real rs(1000) logical ls(1000) complex cs(500) double precision dabs, erru, dmax1, ws(500) integer temp, temp1, temp2 equivalence (ds(1), cs(1), ws(1), rs(1), is(1), ls(1)) c to get and print the error at each time-step. c for variable inu for rectangle ir c u(nx-kx,ny-ky). c the port library stack and its aliases. call enter(1) c find the error in the solution at 2*kx * 2*ky points / mesh rectangle. c x search grid. ixs = idlumd(ws(ix), nx, 2*kx, nxs) c y search grid. iys = idlumd(ws(iy), ny, 2*ky, nys) c u search grid values. iewe = istkgt(nxs*nys, 4) c the exact solution. call ewe2(t, ws(ixs), nxs, ws(iys), nys, ws(iewe), inu, ir) ka(1) = kx ka(2) = ky ita(1) = ix ita(2) = iy nta(1) = nx nta(2) = ny ixa(1) = ixs ixa(2) = iys nxa(1) = nxs nxa(2) = nys ma(1) = 0 c get solution. ma(2) = 0 c approximate solution values. ifa = istkgt(nxs*nys, 4) c evaluate them. call dtsd1(2, ka, ws, ita, nta, u, ws, ixa, nxa, ma, ws(ifa)) c error in solution values. erru = 0 temp = nxs*nys do 1 i = 1, temp temp2 = iewe+i temp1 = ifa+i erru = dmax1(erru, dabs(ws(temp2-1)-ws(temp1-1))) 1 continue temp = i1mach(2) write (temp, 2) ir, inu, erru 2 format(9h for rect,i3,14h error in u(.,, i2, 1 3h) =, 1pe10.2) call leave return end