C\$TEST DTTGU1 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)) c since idumb places the meshes in the port stack, the name of c the port stack, ws, is used as the x and y arrays 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) 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 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 c the exact solution. do 2 i = 1, nx do 1 j = 1, ny u(i, j) = t*x(i)*y(j) 1 continue 2 continue return end