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oneilmoneilm
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added file for laplace modal greens functions
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‎chunkie/+chnk/+axissymlap2d/g0funcall.m‎

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function [gvals, gdzs, gdrs, gdrps] = g0funcall(r, rp, dr, z, zp, dz, maxm)
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%
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% chnk.axissymlap2d.g0funcall evaluates a collection of axisymmetric Laplace
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% Green's functions, defined by the expression:
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%
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% gfunc(n) = pi*rp * \int_0^{2\pi} 1/|x - x'| e^(-i n t) dt
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%
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% The extra factor of rp (and maybe pi?) out front makes subsequent interfacing
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% with RCIP slightly easier. Modes 0 through maxm are returned, with gval(1) =
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% mode 0 and gval(maxm+1) = mode maxm. The function is even, so g_{-n} = g_n.
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%
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% The above scaling should be consistent with what is in
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% chnk.axissymlap2d.gfunc, which is for merely the zero-mode
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%
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twopi = 2*pi;
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fourpi = 4*pi;
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done = 1.0;
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ima = 1i;
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%r = targ(1)
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%z = targ(2)
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r0 = rp;
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z0 = zp;
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rzero = sqrt(r*r + r0*r0 + dz*dz);
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alpha = 2*r*r0/rzero^2;
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x = 1/alpha;
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xminus = (dr*dr + dz*dz)/2/r/r0;
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dxdr = (r^2 - r0^2 - (dz)^2)/2/r0/r^2
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dxdz = 2*(dz)/2/r/r0
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dxdr0 = (r0^2 - r^2 - (dz)^2)/2/r/r0^2
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dxdz0 = -dxdz
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%!
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%! if xminus is very small, use the forward recurrence
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%!
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%!!!!print *, 'inside g0mall, x = ', x
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iffwd = 0
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if (x < 1.005)
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iffwd = 1
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if ((x >= 1.0005d0) && (maxm > 163))
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iffwd = 0;
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end
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if ((x >= 1.00005d0) && (maxm > 503))
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iffwd = 0;
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end
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if ((x >= 1.000005d0) && (maxm > 1438))
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iffwd = 0;
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end
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if ((x >= 1.0000005d0) && (maxm > 4380))
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iffwd = 0;
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end
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if ((x >= 1.00000005d0) && (maxm > 12307))
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iffwd = 0;
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end
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end
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if (iffwd = 1)
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%!!xminus = .000005d0
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%!!x = 1 + xminus
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call axi_q2lege01(x, xminus, q0, q1, dq0, dq1)
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done = 1
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half = done/2
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%pi = 4*atan(done)
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fac = done/sqrt(r*r0)/4/pi^2
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vals(0) = q0
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vals(1) = q1
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derprev = dq0
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der = dq1
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grads(1,0) = (dq0*dxdr - q0/2/r)
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grads(1,1) = (dq1*dxdr - q1/2/r)
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grads(2,0) = dq0*dxdz
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grads(2,1) = dq1*dxdz
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grad0s(1,0) = (dq0*dxdr0 - q0/2/r0)
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grad0s(1,1) = (dq1*dxdr0 - q1/2/r0)
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grad0s(2,0) = dq0*dxdz0
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grad0s(2,1) = dq1*dxdz0
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for i = 1:(maxm-1)
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vals(i+1) = (2*i*x*vals(i) - (i-half)*vals(i-1))/(i+half)
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dernext = (2*i*(vals(i)+x*der) - (i-half)*derprev)/(i+half)
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grads(1,i+1) = (dernext*dxdr - vals(i+1)/2/r)
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grads(2,i+1) = dernext*dxdz
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grad0s(1,i+1) = (dernext*dxdr0 - vals(i+1)/2/r0)
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grad0s(2,i+1) = dernext*dxdz0
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derprev = der
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der = dernext
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%! if (abs(vals(i+1)) > abs(vals(i))) then
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%! print *
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%! print *
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%! call prin2('x = *', x, 1)
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%! call prinf('i = *', i, 1)
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%! call prin2('vals(i+1) = *', vals(i+1), 1)
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%! call prin2('vals(i) = *', vals(i), 1)
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%! stop
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%! endif
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end
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for i = 0:maxm
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vals(i) = vals(i)*fac
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grads(1,i) = grads(1,i)*fac
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grads(2,i) = grads(2,i)*fac
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grad0s(1,i) = grad0s(1,i)*fac
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grad0s(2,i) = grad0s(2,i)*fac
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vals(-i) = vals(i)
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grads(1,-i) = grads(1,i)
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grads(2,-i) = grads(2,i)
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grad0s(1,-i) = grad0s(1,i)
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grad0s(2,-i) = grad0s(2,i)
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end
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return
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end
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%!
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%! if here, xminus > .005, so run forward and backward recurrence
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%!
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%!
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%! run the recurrence, starting from maxm, until it has exploded
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%! for BOTH the values and derivatives
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%!
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done = 1
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half = done/2
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f = 1
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fprev = 0
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der = 1
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derprev = 0
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maxiter = 100000
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upbound = 1.0d19
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for i = maxm:maxiter
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fnext = (2*i*x*f - (i-half)*fprev)/(i+half)
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dernext = (2*i*(x*der+f) - (i-half)*derprev)/(i+half)
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if (abs(fnext) .ge. upbound)
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if (abs(dernext) .ge. upbound)
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nterms = i+1
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exit
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end
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end
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fprev = f
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f = fnext
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derprev = der
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der = dernext
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end
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%!
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%! now start at nterms and recurse down to maxm
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%!
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if (nterms .lt. 10) then
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nterms = 10
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end
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fnext = 0
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f = 1
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dernext = 0
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der = 1
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%555
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% Make correct downwrd recurrence
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for i = nterm,maxm,-1
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fprev = (2*i*x*f - (i+half)*fnext)/(i-half)
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fnext = f
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f = fprev
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derprev = (2*i*(x*der+f) - (i+half)*dernext)/(i-half)
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dernext = der
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der = derprev
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enddo
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vals(maxm-1) = f
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vals(maxm) = fnext
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ders(maxm-1) = der
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ders(maxm) = dernext
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do i = maxm-1,1,-1
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vals(i-1) = (2*i*x*vals(i) - (i+half)*vals(i+1))/(i-half)
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ders(i-1) = (2*i*(x*ders(i)+vals(i)) &
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- (i+half)*ders(i+1))/(i-half)
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end do
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!
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! normalize the values, and use a formula for the derivatives
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!
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call axi_q2lege01(x, xminus, q0, q1, dq0, dq1)
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done = 1
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pi = 4*atan(done)
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ratio = q0/vals(0)
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do i = 0,maxm
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vals(i) = vals(i)*ratio
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enddo
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ders(0) = dq0
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ders(1) = dq1
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do i = 2,maxm
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ders(i) = -(i-.5d0)*(vals(i-1) - x*vals(i))/(1+x)/xminus
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end do
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!
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! and scale everyone...
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!
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fac = 1/sqrt(r*r0)/4/pi^2
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do i = 0,maxm
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grads(1,i) = (ders(i)*dxdr - vals(i)/2/r)*fac
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grads(2,i) = ders(i)*dxdz*fac
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grad0s(1,i) = (ders(i)*dxdr0 - vals(i)/2/r0)*fac
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grad0s(2,i) = ders(i)*dxdz0*fac
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vals(i) = vals(i)*fac
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vals(-i) = vals(i)
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grads(1,-i) = grads(1,i)
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grads(2,-i) = grads(2,i)
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grad0s(1,-i) = grad0s(1,i)
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grad0s(2,-i) = grad0s(2,i)
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end do
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end

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