C$TEST DTTGR5 c main program common /cstak/ ds double precision ds(350000) external handle, bc, af integer ndx, ndy, istkgt, i, is(1000), iu integer ix, iy, nu, kx, nx, ky integer ny real errpar(2), rs(1000), float logical ls(1000) complex cs(500) double precision tstart, dble, dt, lx, ly, rx double precision ry, ws(500), tstop integer temp, temp1 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 lx = 0 rx = 1 ly = 0 ry = 1 kx = 4 ky = 4 ndx = 2 ndy = 2 tstart = 0 tstop = 1 dt = 1 errpar(1) = 1e-2 errpar(2) = 1e-4 nx = ndx+2*(kx-1) c space for x mesh. ix = istkgt(nx, 4) do 1 i = 1, kx temp = ix+i ws(temp-1) = 0 temp = ix+nx-i ws(temp) = rx 1 continue c 0 and rx mult = kx. 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 ny = ndy+2*(ky-1) c space for y mesh. iy = istkgt(ny, 4) do 3 i = 1, ky temp = iy+i ws(temp-1) = 0 temp = iy+ny-i ws(temp) = ry 3 continue c 0 and ry mult = ky. temp = ndy-1 do 4 i = 1, temp temp1 = iy+ky-2+i ws(temp1) = ry*(dble(float(i-1))/(dble(float(ndy))-1d0))**ky 4 continue c space for the solution. iu = istkgt(nu*(nx-kx)*(ny-ky), 4) call setd(nu*(nx-kx)*(ny-ky), 0d0, ws(iu)) call dttgr(ws(iu), nu, kx, ws(ix), nx, ky, ws(iy), ny, tstart, 1 tstop, dt, af, bc, errpar, handle) 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 handle(t0, u0, t, u, nv, dt, tstop) integer nv double precision t0, u0(nv), t, u(nv), dt, tstop common /d7tgrp/ errpar, nu, mxq, myq integer nu, mxq, myq real errpar(2) common /d7tgrm/ kx, ix, nx, ky, iy, ny integer kx, ix, nx, ky, iy, ny if (t0 .ne. t) goto 2 write (6, 1) t 1 format (16h restart for t =, 1pe10.2) return 2 call gerr(kx, ix, nx, ky, iy, ny, u, nu, t) return end subroutine gerr(kx, ix, nx, ky, iy, ny, u, nu, t) integer kx, ix, nx, ky, iy, ny integer nu 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 u(nx-kx,ny-ky,nu). 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 ewe(t, ws(ixs), nxs, ws(iys), nys, ws(iewe), nu) 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) t, erru 2 format (14h error in u(.,, 1pe10.2, 3h) =, 1pe10.2) call leave return end subroutine ewe(t, x, nx, y, ny, u, nu) integer nu, nx, ny double precision t, x(nx), y(ny), u(nx, ny, nu) integer i, j, p double precision r, dcos, dlog, dsin, datan, theta double precision dsqrt c the exact solution. do 7 p = 1, nu 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, p) = r*(dcos(theta)*dlog(r)-theta*dsin(theta)) goto 4 3 u(i, j, p) = 0 4 continue 5 continue 6 continue 7 continue return end