User: eschnett
Date: 2012/06/16 10:39 AM
Added:
/trunk/test/
test_driscollhealy.par
/trunk/test/test_driscollhealy/
mp_harmonic_im_r8.00.ph.asc, mp_harmonic_im_r8.00.th.asc, mp_harmonic_l0_m0_r8.00.asc, mp_harmonic_l1_m-1_r8.00.asc, mp_harmonic_l1_m0_r8.00.asc, mp_harmonic_l1_m1_r8.00.asc, mp_harmonic_l2_m-1_r8.00.asc, mp_harmonic_l2_m-2_r8.00.asc, mp_harmonic_l2_m0_r8.00.asc, mp_harmonic_l2_m1_r8.00.asc, mp_harmonic_l2_m2_r8.00.asc, mp_harmonic_re_r8.00.ph.asc, mp_harmonic_re_r8.00.th.asc, test_driscollhealy.par
Modified:
/trunk/
param.ccl
/trunk/src/
integrate.cc, integrate.hh, utils.cc
Log:
Implement Driscoll&Healy integration
Implements a more accurate integration over the sphere using an
algorithm by Driscoll & Healy. This algorithm uses Gaussian
integration weights, leading (almost) to exponential convergence.
File Changes:
Directory: /trunk/src/
======================
File [modified]: integrate.cc
Delta lines: +48 -1
===================================================================
--- trunk/src/integrate.cc 2012-05-28 22:20:58 UTC (rev 82)
+++ trunk/src/integrate.cc 2012-06-16 15:39:07 UTC (rev 83)
@@ -107,6 +107,52 @@
return ((double) 1 / (double) 9) * hx * hy * integrand_sum;
}
+// See: J.R. Driscoll and D.M. Healy Jr., Computing Fourier transforms
+// and convolutions on the 2-sphere. Advances in Applied Mathematics,
+// 15(2):202–250, 1994.
+CCTK_REAL DriscollHealy2DIntegral(CCTK_REAL const *const f,
+ int const nx, int const ny,
+ CCTK_REAL const hx, CCTK_REAL const hy)
+{
+ assert(f);
+ assert(nx >= 0);
+ assert(ny >= 0);
+ assert(nx % 2 == 0);
+
+ CCTK_REAL integrand_sum = 0.0;
+
+ // Skip the poles (ix=0 and ix=nx), since the weight there is zero
+ // anyway
+#pragma omp parallel for reduction(+: integrand_sum)
+ for (int ix = 1; ix < nx; ++ ix)
+ {
+
+ // These weights lead to an almost spectral convergence
+ CCTK_REAL const theta = M_PI * ix / nx;
+ CCTK_REAL weight = 0.0;
+ for (int l = 0; l < nx/2; ++ l)
+ {
+ weight += sin((2*l+1)*theta)/(2*l+1);
+ }
+ weight *= 4.0 / M_PI;
+
+ CCTK_REAL local_sum = 0.0;
+ // Skip the last point (iy=ny), since we assume periodicity and
+ // therefor it has the same value as the first point. We don't use
+ // weights in this direction, which leads to spectral convergence.
+ // (Yay periodicity!)
+ for (int iy = 0; iy < ny; ++ iy)
+ {
+ local_sum += f[idx(ix,iy)];
+ }
+
+ integrand_sum += weight * local_sum;
+
+ }
+
+ return hx * hy * integrand_sum;
+}
+
// 1D integrals
static CCTK_REAL Simpson1DIntegral(CCTK_REAL const *f, int n, CCTK_REAL h)
@@ -114,7 +160,8 @@
CCTK_REAL integrand_sum = 0;
int i = 0;
- assert(n > 0); assert(f);
+ assert(f);
+ assert(n > 0);
assert(n % 2 == 0);
int p = n / 2;
File [modified]: integrate.hh
Delta lines: +3 -0
===================================================================
--- trunk/src/integrate.hh 2012-05-28 22:20:58 UTC (rev 82)
+++ trunk/src/integrate.hh 2012-06-16 15:39:07 UTC (rev 83)
@@ -6,4 +6,7 @@
CCTK_REAL Simpson2DIntegral(CCTK_REAL const *f, int nx, int ny,
CCTK_REAL hx, CCTK_REAL hy);
+CCTK_REAL DriscollHealy2DIntegral(CCTK_REAL const *f, int nx, int ny,
+ CCTK_REAL hx, CCTK_REAL hy);
+
#endif
File [modified]: utils.cc
Delta lines: +28 -3
===================================================================
--- trunk/src/utils.cc 2012-05-28 22:20:58 UTC (rev 82)
+++ trunk/src/utils.cc 2012-06-16 15:39:07 UTC (rev 83)
@@ -346,7 +346,8 @@
*outim = tempi;
}
}
- else if (CCTK_Equals(integration_method, "simpson"))
+ else if (CCTK_Equals(integration_method, "Simpson") ||
+ CCTK_Equals(integration_method, "DriscollHealy"))
{
static CCTK_REAL *fr = 0;
static CCTK_REAL *fi = 0;
@@ -368,7 +369,31 @@
array1i[i] * array2r[i] ) * sin(th[i]);
}
- *outre = Simpson2DIntegral(fr, ntheta, nphi, dth, dph);
- *outim = Simpson2DIntegral(fi, ntheta, nphi, dth, dph);
+ if (CCTK_Equals(integration_method, "Simpson"))
+ {
+ if (nphi % 2 != 0 || ntheta % 2 != 0)
+ {
+ CCTK_WARN (CCTK_WARN_ABORT, "The Simpson integration method requires even ntheta and even nphi");
+ }
+ *outre = Simpson2DIntegral(fr, ntheta, nphi, dth, dph);
+ *outim = Simpson2DIntegral(fi, ntheta, nphi, dth, dph);
+ }
+ else if (CCTK_Equals(integration_method, "DriscollHealy"))
+ {
+ if (ntheta % 2 != 0)
+ {
+ CCTK_WARN (CCTK_WARN_ABORT, "The Driscoll&Healy integration method requires even ntheta");
+ }
+ *outre = DriscollHealy2DIntegral(fr, ntheta, nphi, dth, dph);
+ *outim = DriscollHealy2DIntegral(fi, ntheta, nphi, dth, dph);
+ }
+ else
+ {
+ CCTK_WARN(CCTK_WARN_ABORT, "internal error");
+ }
}
+ else
+ {
+ CCTK_WARN(CCTK_WARN_ABORT, "internal error");
+ }
}
Directory: /trunk/test/
=======================
File [added]: test_driscollhealy.par
Delta lines: +89 -0
===================================================================
--- trunk/test/test_driscollhealy.par (rev 0)
+++ trunk/test/test_driscollhealy.par 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1,89 @@
+
+ActiveThorns = "CoordBase SymBase Boundary CartGrid3d IOUtil Carpet CarpetLib CarpetInterp AEILocalInterp InitBase Multipole LoopControl"
+
+#############################################################
+# Grid
+#############################################################
+
+CartGrid3D::type = "coordbase"
+CartGrid3D::domain = "full"
+CartGrid3D::avoid_origin = "no"
+
+CoordBase::domainsize = minmax
+CoordBase::xmin = -10
+CoordBase::ymin = -10
+CoordBase::zmin = -10
+CoordBase::xmax = 10
+CoordBase::ymax = 10
+CoordBase::zmax = 10
+CoordBase::dx = 0.2
+CoordBase::dy = 0.2
+CoordBase::dz = 0.2
+CoordBase::boundary_size_x_lower = 2
+CoordBase::boundary_size_y_lower = 2
+CoordBase::boundary_size_z_lower = 2
+CoordBase::boundary_shiftout_x_lower = 0
+CoordBase::boundary_shiftout_y_lower = 0
+CoordBase::boundary_shiftout_z_lower = 0
+CoordBase::boundary_size_x_upper = 2
+CoordBase::boundary_size_y_upper = 2
+CoordBase::boundary_size_z_upper = 2
+CoordBase::boundary_shiftout_x_upper = 0
+CoordBase::boundary_shiftout_y_upper = 0
+CoordBase::boundary_shiftout_z_upper = 0
+
+#############################################################
+# Carpet
+#############################################################
+
+Carpet::ghost_size = 3
+Carpet::domain_from_coordbase = "yes"
+Carpet::poison_new_timelevels = "yes"
+Carpet::check_for_poison = "no"
+CarpetLib::poison_value = 113
+Carpet::init_fill_timelevels = "yes"
+
+#############################################################
+# CarpetLib
+#############################################################
+
+CarpetLib::poison_new_memory = "yes"
+
+#############################################################
+# Cactus
+#############################################################
+
+Cactus::terminate = "iteration"
+Cactus::cctk_itlast = 0
+
+#############################################################
+# Multipole
+#############################################################
+
+Multipole::nradii = 1
+Multipole::radius[0] = 8.0
+Multipole::variables = "Multipole::harmonic_re{sw=-2 cmplx='Multipole::harmonic_im' name='harmonic'}"
+Multipole::integration_method = "DriscollHealy"
+
+Multipole::enable_test = "yes"
+Multipole::test_l = 2
+Multipole::test_m = 2
+Multipole::out_1d_every = 1
+
+#############################################################
+# Output
+#############################################################
+
+IO::out_dir = $parfile
+IO::out_fileinfo = "none"
+
+# Enabling 1D output for the test grid functions would be helpful for
+# localising any failures but it makes the tests dependent on the
+# number of processors, as CarpetIOASCII's output is dependent on
+# this.
+
+# CarpetIOASCII::out1d_vars = "Multipole::harmonics"
+# CarpetIOASCII::out1d_every = 1
+# CarpetIOASCII::out1d_x = yes
+# CarpetIOASCII::out1d_y = yes
+# CarpetIOASCII::out1d_z = yes
Directory: /trunk/test/test_driscollhealy/
==========================================
File [added]: mp_harmonic_im_r8.00.ph.asc
Delta lines: +104 -0
===================================================================
--- trunk/test/test_driscollhealy/mp_harmonic_im_r8.00.ph.asc (rev 0)
+++ trunk/test/test_driscollhealy/mp_harmonic_im_r8.00.ph.asc 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1,104 @@
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File [added]: mp_harmonic_im_r8.00.th.asc
Delta lines: +55 -0
===================================================================
--- trunk/test/test_driscollhealy/mp_harmonic_im_r8.00.th.asc (rev 0)
+++ trunk/test/test_driscollhealy/mp_harmonic_im_r8.00.th.asc 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1,55 @@
+"Time = 0
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+
File [added]: mp_harmonic_l0_m0_r8.00.asc
Delta lines: +1 -0
===================================================================
--- trunk/test/test_driscollhealy/mp_harmonic_l0_m0_r8.00.asc (rev 0)
+++ trunk/test/test_driscollhealy/mp_harmonic_l0_m0_r8.00.asc 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1 @@
+0.000000 0 0
File [added]: mp_harmonic_l1_m-1_r8.00.asc
Delta lines: +1 -0
===================================================================
--- trunk/test/test_driscollhealy/mp_harmonic_l1_m-1_r8.00.asc (rev 0)
+++ trunk/test/test_driscollhealy/mp_harmonic_l1_m-1_r8.00.asc 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1 @@
+0.000000 0 0
File [added]: mp_harmonic_l1_m0_r8.00.asc
Delta lines: +1 -0
===================================================================
--- trunk/test/test_driscollhealy/mp_harmonic_l1_m0_r8.00.asc (rev 0)
+++ trunk/test/test_driscollhealy/mp_harmonic_l1_m0_r8.00.asc 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1 @@
+0.000000 0 0
File [added]: mp_harmonic_l1_m1_r8.00.asc
Delta lines: +1 -0
===================================================================
--- trunk/test/test_driscollhealy/mp_harmonic_l1_m1_r8.00.asc (rev 0)
+++ trunk/test/test_driscollhealy/mp_harmonic_l1_m1_r8.00.asc 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1 @@
+0.000000 0 0
File [added]: mp_harmonic_l2_m-1_r8.00.asc
Delta lines: +1 -0
===================================================================
--- trunk/test/test_driscollhealy/mp_harmonic_l2_m-1_r8.00.asc (rev 0)
+++ trunk/test/test_driscollhealy/mp_harmonic_l2_m-1_r8.00.asc 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1 @@
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File [added]: mp_harmonic_l2_m-2_r8.00.asc
Delta lines: +1 -0
===================================================================
--- trunk/test/test_driscollhealy/mp_harmonic_l2_m-2_r8.00.asc (rev 0)
+++ trunk/test/test_driscollhealy/mp_harmonic_l2_m-2_r8.00.asc 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1 @@
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File [added]: mp_harmonic_l2_m0_r8.00.asc
Delta lines: +1 -0
===================================================================
--- trunk/test/test_driscollhealy/mp_harmonic_l2_m0_r8.00.asc (rev 0)
+++ trunk/test/test_driscollhealy/mp_harmonic_l2_m0_r8.00.asc 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1 @@
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File [added]: mp_harmonic_l2_m1_r8.00.asc
Delta lines: +1 -0
===================================================================
--- trunk/test/test_driscollhealy/mp_harmonic_l2_m1_r8.00.asc (rev 0)
+++ trunk/test/test_driscollhealy/mp_harmonic_l2_m1_r8.00.asc 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1 @@
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File [added]: mp_harmonic_l2_m2_r8.00.asc
Delta lines: +1 -0
===================================================================
--- trunk/test/test_driscollhealy/mp_harmonic_l2_m2_r8.00.asc (rev 0)
+++ trunk/test/test_driscollhealy/mp_harmonic_l2_m2_r8.00.asc 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1 @@
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File [added]: mp_harmonic_re_r8.00.ph.asc
Delta lines: +104 -0
===================================================================
--- trunk/test/test_driscollhealy/mp_harmonic_re_r8.00.ph.asc (rev 0)
+++ trunk/test/test_driscollhealy/mp_harmonic_re_r8.00.ph.asc 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1,104 @@
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+6.283185 0.476896019094934509
+
+
File [added]: mp_harmonic_re_r8.00.th.asc
Delta lines: +55 -0
===================================================================
--- trunk/test/test_driscollhealy/mp_harmonic_re_r8.00.th.asc (rev 0)
+++ trunk/test/test_driscollhealy/mp_harmonic_re_r8.00.th.asc 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1,55 @@
+"Time = 0
+0.000000 -4.885011147332195149e-16
+0.061600 0.6225628802689283647
+0.123200 0.626011174765530698
+0.184800 0.6200885652671891402
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+3.079993 5.663901966311766602e-07
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+
+
File [added]: test_driscollhealy.par
Delta lines: +90 -0
===================================================================
--- trunk/test/test_driscollhealy/test_driscollhealy.par (rev 0)
+++ trunk/test/test_driscollhealy/test_driscollhealy.par 2012-06-16 15:39:07 UTC (rev 83)
@@ -0,0 +1,90 @@
+
+ActiveThorns = "CoordBase SymBase Boundary CartGrid3d IOUtil Carpet CarpetLib CarpetInterp AEILocalInterp InitBase Multipole LoopControl"
+
+#############################################################
+# Grid
+#############################################################
+
+CartGrid3D::type = "coordbase"
+CartGrid3D::domain = "full"
+CartGrid3D::avoid_origin = "no"
+
+CoordBase::domainsize = minmax
+CoordBase::xmin = -10
+CoordBase::ymin = -10
+CoordBase::zmin = -10
+CoordBase::xmax = 10
+CoordBase::ymax = 10
+CoordBase::zmax = 10
+CoordBase::dx = 0.2
+CoordBase::dy = 0.2
+CoordBase::dz = 0.2
+CoordBase::boundary_size_x_lower = 2
+CoordBase::boundary_size_y_lower = 2
+CoordBase::boundary_size_z_lower = 2
+CoordBase::boundary_shiftout_x_lower = 0
+CoordBase::boundary_shiftout_y_lower = 0
+CoordBase::boundary_shiftout_z_lower = 0
+CoordBase::boundary_size_x_upper = 2
+CoordBase::boundary_size_y_upper = 2
+CoordBase::boundary_size_z_upper = 2
+CoordBase::boundary_shiftout_x_upper = 0
+CoordBase::boundary_shiftout_y_upper = 0
+CoordBase::boundary_shiftout_z_upper = 0
+
+#############################################################
+# Carpet
+#############################################################
+
+Carpet::ghost_size = 3
+Carpet::domain_from_coordbase = "yes"
+Carpet::poison_new_timelevels = "yes"
+Carpet::check_for_poison = "no"
+CarpetLib::poison_value = 113
+Carpet::init_fill_timelevels = "yes"
+
+#############################################################
+# CarpetLib
+#############################################################
+
+CarpetLib::poison_new_memory = "yes"
+
+#############################################################
+# Cactus
+#############################################################
+
+Cactus::terminate = "iteration"
+Cactus::cctk_itlast = 0
+
+#############################################################
+# Multipole
+#############################################################
+
+Multipole::nradii = 1
+Multipole::ntheta = 51
+Multipole::radius[0] = 8.0
+Multipole::variables = "Multipole::harmonic_re{sw=-2 cmplx='Multipole::harmonic_im' name='harmonic'}"
+Multipole::integration_method = "DriscollHealy"
+
+Multipole::enable_test = "yes"
+Multipole::test_l = 2
+Multipole::test_m = 2
+Multipole::out_1d_every = 1
+
+#############################################################
+# Output
+#############################################################
+
+IO::out_dir = $parfile
+IO::out_fileinfo = "none"
+
+# Enabling 1D output for the test grid functions would be helpful for
+# localising any failures but it makes the tests dependent on the
+# number of processors, as CarpetIOASCII's output is dependent on
+# this.
+
+# CarpetIOASCII::out1d_vars = "Multipole::harmonics"
+# CarpetIOASCII::out1d_every = 1
+# CarpetIOASCII::out1d_x = yes
+# CarpetIOASCII::out1d_y = yes
+# CarpetIOASCII::out1d_z = yes
Directory: /trunk/
==================
File [modified]: param.ccl
Delta lines: +3 -2
===================================================================
--- trunk/param.ccl 2012-05-28 22:20:58 UTC (rev 82)
+++ trunk/param.ccl 2012-06-16 15:39:07 UTC (rev 83)
@@ -29,8 +29,9 @@
KEYWORD integration_method "How to do surface integrals" STEERABLE=always
{
- "midpoint" :: "Midpoint rule (1st order)"
- "Simpson" :: "Simpson's rule (4th order)"
+ "midpoint" :: "Midpoint rule (1st order)"
+ "Simpson" :: "Simpson's rule (4th order) [requires even ntheta and nphi]"
+ "DriscollHealy" :: "Driscoll & Healy (exponentially convergent) [requires even ntheta]"
} "midpoint"
CCTK_INT out_every "How often to output" \
