C\$TEST DPOST6 c main program common /cstak/ ds double precision ds(4000) common /time/ t double precision t common /param/ vc, x double precision vc(4), x(3) external dee, handle, uofx, bc, af integer ndx, idlumb, istkgt, k, iu, is(1000) integer nu, nv, immmd, imesh, nmesh real errpar(2), rs(1000) logical ls(1000) complex cs(500) double precision tstart, v(4), dt, xb(3), ws(500), tstop equivalence (ds(1), cs(1), ws(1), rs(1), is(1), ls(1)) c to test dpost on the hyperbolic problem c u sub t = - u sub x + g on (-pi,+pi) * (0,pi) c with a moving shock x(t) characterized by c u(x(t)+,t) = 0 and c u(x(t)+,t) - u(x(t)-,t) = x'(t) c where g is chosen so that the solution is c sin(x+t) for x < x(t) c u(x,t) = c cos(x+t) for x > x(t) c with x(t) = pi/2 -t . c v(1,2,3) gives the moving mesh and v(4) is the height of the jump. c the port library stack and its aliases. c initialize the port library stack length. call istkin(4000, 4) call enter(1) nu = 1 nv = 4 errpar(1) = 0 c absolute error. errpar(2) = 1e-2 tstart = 0 tstop = 3.14 dt = 0.4 k = 4 c ndx uniform mesh points on each interval of xb. ndx = 6 xb(1) = 0 xb(2) = 1 xb(3) = 2 c get mesh on port stack. imesh = idlumb(xb, 3, ndx, k, nmesh) c make 1 of multiplicity k-1. imesh = immmd(imesh, nmesh, 1d0, k-1) x(1) = -3.14 x(2) = 3.14/2. x(3) = 3.14 c initial values for v. call dlplmg(3, x, vc) c get u on the port stack. iu = istkgt(nmesh-k, 4) c uofx needs time. t = tstart c the initial height of the jump. vc(4) = 1 c uofx needs v for mapping. call movefd(nv, vc, v) c initial conditions for u. call dl2sff(uofx, k, ws(imesh), nmesh, ws(iu)) c output ics. call handle(t-1d0, ws(iu), v, t, ws(iu), v, nu, nmesh-k, nv, k, 1 ws(imesh), nmesh, dt, tstop) call dpost(ws(iu), nu, k, ws(imesh), nmesh, v, nv, tstart, tstop 1 , dt, af, bc, dee, errpar, handle) call leave call wrapup stop end subroutine af(t, xi, nx, u, ux, ut, utx, nu, v, vt, nv, a, 1 au, aux, aut, autx, av, avt, f, fu, fux, fut, futx, fv, fvt) integer nu, nv, nx double precision t, xi(nx), u(nx, nu), ux(nx, nu), ut(nx, nu), 1 utx(nx, nu) double precision v(nv), vt(nv), a(nx, nu), au(nx, nu, nu), aux(nx, 1 nu, nu), aut(nx, nu, nu) double precision autx(nx, nu, nu), av(nx, nu, nv), avt(nx, nu, nv) 1 , f(nx, nu), fu(nx, nu, nu), fux(nx, nu, nu) double precision fut(nx, nu, nu), futx(nx, nu, nu), fv(nx, nu, nv) 1 , fvt(nx, nu, nv) common /dpostf/ failed logical failed integer i double precision xxi(99), xtv(99), xvv(99), x(99), dcos, dsin double precision xxiv(99), ax(99), fx(99), xt(99), xv(99) logical temp temp = v(2) .le. v(1) if (.not. temp) temp = v(2) .ge. v(3) if (.not. temp) goto 1 failed = .true. return c map xi into x. 1 call dlplm(xi, nx, v, 3, x, xxi, xxiv, xv, xvv, xt, xtv) c map u into x system. call dpostu(xi, x, xt, xxi, xv, vt, nx, 3, ux, ut, nu, ax, fx) do 4 i = 1, nx a(i, 1) = -u(i, 1) au(i, 1, 1) = -1 f(i, 1) = ut(i, 1) fut(i, 1, 1) = 1 if (xi(i) .gt. 1d0) goto 2 f(i, 1) = f(i, 1)-2d0*dcos(x(i)+t) fx(i) = 2d0*dsin(x(i)+t) goto 3 2 f(i, 1) = f(i, 1)-vt(4) fvt(i, 1, 4) = -1 f(i, 1) = f(i, 1)+2d0*dsin(x(i)+t) fx(i) = 2d0*dcos(x(i)+t) 3 continue 4 continue c map a and f into xi system. call dposti(xi, x, xt, xxi, xv, xtv, xxiv, xvv, nx, ux, ut, nu, v, 1 vt, nv, 1, 3, a, ax, au, aux, aut, autx, av, avt, f, fx, fu, 2 fux, fut, futx, fv, fvt) return end subroutine bc(t, l, r, u, ux, ut, utx, nu, v, vt, nv, b, bu, 1 bux, but, butx, bv, bvt) integer nu, nv double precision t, l, r, u(nu, 2), ux(nu, 2), ut(nu, 2) double precision utx(nu, 2), v(nv), vt(nv), b(nu, 2), bu(nu, nu, 2 1 ), bux(nu, nu, 2) double precision but(nu, nu, 2), butx(nu, nu, 2), bv(nu, nv, 2), 1 bvt(nu, nv, 2) double precision dsin b(1, 1) = u(1, 1)-dsin(t-3.14) c u(-pi,t) = sin(-pi+t). bu(1, 1, 1) = 1 return end subroutine dee(t, k, x, nx, u, ut, nu, nxmk, v, vt, nv, d, 1 du, dut, dv, dvt) integer nxmk, nu, nv, nx integer k double precision t, x(nx), u(nxmk, nu), ut(nxmk, nu), v(nv), vt( 1 nv) double precision d(nv), du(nv, nxmk, nu), dut(nv, nxmk, nu), dv( 1 nv, nv), dvt(nv, nv) integer intrvd, i, ileft double precision bx(10), xx(1), d1mach integer temp d(1) = v(1)+3.14 c x(0,v) = -pi. dv(1, 1) = 1 c xx(1) = 1 + a rounding error. xx(1) = d1mach(4)+1d0 ileft = intrvd(nx, x, xx(1)) c get the b-spline basis at xx. call dbspln(k, x, nx, xx, 1, ileft, bx) d(2) = -v(4) c u(x(t)+,t) - jump = 0. dv(2, 4) = -1 do 1 i = 1, k temp = ileft+i-k d(2) = d(2)+u(temp, 1)*bx(i) temp = ileft+i-k du(2, temp, 1) = bx(i) 1 continue d(3) = v(3)-3.14 c x(2,v) = +pi. dv(3, 3) = 1 c jump + d( x(1,v(t)) )/dt = 0. d(4) = vt(2)+v(4) dvt(4, 2) = 1 dv(4, 4) = 1 return end subroutine handle(t0, u0, v0, t, u, v, nu, nxmk, nv, k, x, 1 nx, dt, tstop) integer nxmk, nu, nv, nx integer k double precision t0, u0(nxmk, nu), v0(nv), t, u(nxmk, nu), v(nv) double precision x(nx), dt, tstop common /param/ vc, xx double precision vc(4), xx(3) common /time/ tt double precision tt external uofx integer i1mach double precision deesff, eu, ev(2) integer temp c output and checking routine. if (t0 .ne. t) goto 2 temp = i1mach(2) write (temp, 1) t, dt 1 format (16h restart for t =, 1pe10.2, 7h dt =, 1pe10.2) return 2 tt = t c uofx needs v for mapping. call movefd(nv, v, vc) eu = deesff(k, x, nx, u, uofx) c error in position of shock. ev(1) = v(2)-(3.14/2.-t) c error in height of shock. ev(2) = v(4)-1d0 temp = i1mach(2) write (temp, 3) t, eu, ev 3 format (14h error in u(x,, 1pe10.2, 4h ) =, 1pe10.2, 6h v =, 2( 1 1pe10.2)) return end subroutine uofx(xi, nx, u, w) integer nx double precision xi(nx), u(nx), w(nx) common /cstak/ ds double precision ds(500) common /param/ vc, x double precision vc(4), x(3) common /time/ t double precision t integer ixv, ixx, istkgt, i, is(1000) real rs(1000) logical ls(1000) complex cs(500) double precision ewe, ws(500) integer temp equivalence (ds(1), cs(1), ws(1), rs(1), is(1), ls(1)) c the port library stack and its aliases. call enter(1) ixx = istkgt(nx, 4) c space for x and xv. ixv = istkgt(3*nx, 4) c map into user system. call dlplmx(xi, nx, vc, 3, ws(ixx), ws(ixv)) do 1 i = 1, nx temp = ixx+i u(i) = ewe(t, ws(temp-1), vc(2)) if (xi(i) .gt. 1d0) u(i) = u(i)+1d0 1 continue call leave return end double precision function ewe(t, x, xbreak) double precision t, x, xbreak double precision dcos, dsin if (x .ge. xbreak) goto 1 ewe = dsin(x+t) return 1 if (x .le. xbreak) goto 2 ewe = dcos(x+t) return 2 call seterr(17hewe - x == xbreak, 17, 1, 2) 3 continue 4 stop end