C\$TEST DTTGU1P c main program c to solve the heat equation with solution u == t*x*y, c grad . ( u + ux + .1 * uy, u + uy + .1 * ux ) = ut + ux + uy +g(x,t) common /cstak/ ds double precision ds(350000) integer ixb(4), iyb(4), nxr(4), nyr(4), kxr(4), kyr(4) external handlu, bc, af integer ndx, ndy, istkgt, is(1000), iu, nu, kx, ky, idumb real errpar(2), rs(1000) logical ls(1000) complex cs(500) double precision tstart, dt, tstop, ws(500) c the port library stack and its aliases. equivalence (ds(1), cs(1), ws(1), rs(1), is(1), ls(1)) c initialize the port library stack length. call istkin(350000, 4) call enter(1) nu = 1 kx = 2 ky = 2 ndx = 3 ndy = 3 nr=4 tstart = 0.d0 tstop = 1.d0 dt = 1 errpar(1) = 1e-2 errpar(2) = 1e-4 c uniform grid. c c make grid for t-shaped region c ixb(1) = idumb(-1.0d0, 0.0d0, ndx, kx, nxr(1)) ixb(2) = idumb(0.0d0, 1.0d0, ndx, kx, nxr(2)) ixb(3) = idumb(1.0d0, 2.0d0, ndx, kx, nxr(3)) ixb(4) = idumb(0.0d0, 1.0d0, ndx, kx, nxr(4)) iyb(1) = idumb(0.0d0, 1.0d0, ndy, ky, nyr(1)) iyb(2) = idumb(0.0d0, 1.0d0, ndy, ky, nyr(2)) iyb(3) = idumb(0.0d0, 1.0d0, ndy, ky, nyr(3)) iyb(4) = idumb(-1.0d0, 0.0d0, ndy, ky, nyr(4)) nnu =nu*((nxr(1)-kx)*(nyr(1)+nyr(3)-2*ky)+ 1 (nxr(2)-kx)*(nyr(2)-ky)+ 4 (nxr(4)-kx)*(nyr(4)-ky)) nr=4 c space for the solution. iu = istkgt(nnu, 4) do 1 i=1,nr kxr(i)=kx kyr(i)=ky 1 continue c initial conditions for u. call setd(nnu, 0.d0,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, x, nx, y, ny, nu, u, ut, ux, uy, uxt, uyt 1 , a, au, aut, aux, auy, auxt, auyt, f, fu, fut, fux, fuy, fuxt, 2 fuyt) integer nu, nx, ny double precision t, x(nx), y(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)+.1*uy(p, q, i)+u(p, q, i) a(p, q, i, 2) = uy(p, q, i)+.1*ux(p, q, i)+u(p, q, i) aux(p, q, i, i, 1) = 1 auy(p, q, i, i, 2) = 1 auy(p, q, i, i, 1) = .1 aux(p, q, i, i, 2) = .1 au(p, q, i, i, 1) = 1 au(p, q, i, i, 2) = 1 f(p, q, i) = ut(p, q, i)+ux(p, q, i)+uy(p, q, i) fut(p, q, i, i) = 1 fux(p, q, i, i) = 1 fuy(p, q, i, i) = 1 f(p, q, i) = f(p, q, i)+.2*t-x(p)*y(q) 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 do 2 j = 1, ny do 1 i = 1, nx bu(i, j, 1, 1) = 1 b(i, j, 1) = u(i, j, 1)-t*x(i)*y(j) 1 continue 2 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) c to print the solution at each time-step integer kx, ix, nx, ky, iy, ny integer 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 ka(2), ma(2), is(1000), i1mach real rs(1000) logical ls(1000) complex cs(500) double precision ws(500) integer temp equivalence (ds(1), cs(1), ws(1), rs(1), is(1), ls(1)) c u(nx-kx,ny-ky). c the port library stack and its aliases. call enter(1) c x search grid. c find the solution at 2 * 2 points / mesh rectangle. ixs = idlumd(ws(ix), nx, 2, nxs) c y search grid. iys = idlumd(ws(iy), ny, 2, nys) c u search grid values. 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 ma(2) = 0 c get solution. 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)) temp = i1mach(2) write(temp,9001)ir,inu,(ws(i),i=iFA,IFa+nxs*nys-1) 9001 format(" for rect",i3," u(.,",i2,")=", 1((1p5e10.2/20x,1p4d10.2))) 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 c the exact solution. do 3 p = 1, nu do 2 i = 1, nx do 1 j = 1, ny u(i, j, p) = t*x(i)*y(j) 1 continue 2 continue 3 continue return end