25 August 2014 11:55:21 PM TRIANGLE_FELIPPA_RULE_PRB C++ version Test the TRIANGLE_FELIPPA_RULE library. TRIANGLE_UNIT_MONOMIAL_TEST For the unit triangle, TRIANGLE_UNIT_MONOMIAL returns the exact value of the integral of X^ALPHA Y^BETA Volume = 0.5 ALPHA BETA INTEGRAL 0 0 0.5 0 1 0.166667 0 2 0.0833333 0 3 0.05 0 4 0.0333333 1 0 0.166667 1 1 0.0416667 1 2 0.0166667 1 3 0.00833333 2 0 0.0833333 2 1 0.0166667 2 2 0.00555556 3 0 0.05 3 1 0.00833333 4 0 0.0333333 TRIANGLE_UNIT_QUAD_TEST For the unit triangle, we approximate monomial integrals with: TRIANGLE_UNIT_O01, TRIANGLE_UNIT_O03, TRIANGLE_UNIT_O03b, TRIANGLE_UNIT_O06, TRIANGLE_UNIT_O06b, TRIANGLE_UNIT_O07, TRIANGLE_UNIT_O12, Monomial exponents: 0 0 1 0.5 3 0.5 3 0.5 6 0.5 6 0.5 7 0.5 12 0.5 Exact 0.5 Monomial exponents: 1 0 1 0.166667 3 0.166667 3 0.166667 6 0.166667 6 0.166667 7 0.166667 12 0.166667 Exact 0.166667 Monomial exponents: 0 1 1 0.166667 3 0.166667 3 0.166667 6 0.166667 6 0.166667 7 0.166667 12 0.166667 Exact 0.166667 Monomial exponents: 2 0 1 0.0555556 3 0.0833333 3 0.0833333 6 0.0833333 6 0.0833333 7 0.0833333 12 0.0833333 Exact 0.0833333 Monomial exponents: 1 1 1 0.0555556 3 0.0416667 3 0.0416667 6 0.0416667 6 0.0416667 7 0.0416667 12 0.0416667 Exact 0.0416667 Monomial exponents: 0 2 1 0.0555556 3 0.0833333 3 0.0833333 6 0.0833333 6 0.0833333 7 0.0833333 12 0.0833333 Exact 0.0833333 Monomial exponents: 3 0 1 0.0185185 3 0.0509259 3 0.0416667 6 0.05 6 0.05 7 0.05 12 0.05 Exact 0.05 Monomial exponents: 2 1 1 0.0185185 3 0.0162037 3 0.0208333 6 0.0166667 6 0.0166667 7 0.0166667 12 0.0166667 Exact 0.0166667 Monomial exponents: 1 2 1 0.0185185 3 0.0162037 3 0.0208333 6 0.0166667 6 0.0166667 7 0.0166667 12 0.0166667 Exact 0.0166667 Monomial exponents: 0 3 1 0.0185185 3 0.0509259 3 0.0416667 6 0.05 6 0.05 7 0.05 12 0.05 Exact 0.05 Monomial exponents: 4 0 1 0.00617284 3 0.033179 3 0.0208333 6 0.0333333 6 0.0319444 7 0.0333333 12 0.0333333 Exact 0.0333333 Monomial exponents: 3 1 1 0.00617284 3 0.00887346 3 0.0104167 6 0.00833333 6 0.00902778 7 0.00833333 12 0.00833333 Exact 0.00833333 Monomial exponents: 2 2 1 0.00617284 3 0.00424383 3 0.0104167 6 0.00555556 6 0.00486111 7 0.00555556 12 0.00555556 Exact 0.00555556 Monomial exponents: 1 3 1 0.00617284 3 0.00887346 3 0.0104167 6 0.00833333 6 0.00902778 7 0.00833333 12 0.00833333 Exact 0.00833333 Monomial exponents: 0 4 1 0.00617284 3 0.033179 3 0.0208333 6 0.0333333 6 0.0319444 7 0.0333333 12 0.0333333 Exact 0.0333333 Monomial exponents: 5 0 1 0.00205761 3 0.0219907 3 0.0104167 6 0.0239351 6 0.0208333 7 0.0238095 12 0.0238095 Exact 0.0238095 Monomial exponents: 4 1 1 0.00205761 3 0.00559414 3 0.00520833 6 0.00469912 6 0.00555556 7 0.0047619 12 0.0047619 Exact 0.0047619 Monomial exponents: 3 2 1 0.00205761 3 0.00173611 3 0.00520833 6 0.00239351 6 0.00208333 7 0.00238095 12 0.00238095 Exact 0.00238095 Monomial exponents: 2 3 1 0.00205761 3 0.00173611 3 0.00520833 6 0.00239351 6 0.00208333 7 0.00238095 12 0.00238095 Exact 0.00238095 Monomial exponents: 1 4 1 0.00205761 3 0.00559414 3 0.00520833 6 0.00469912 6 0.00555556 7 0.0047619 12 0.0047619 Exact 0.0047619 Monomial exponents: 0 5 1 0.00205761 3 0.0219907 3 0.0104167 6 0.0239351 6 0.0208333 7 0.0238095 12 0.0238095 Exact 0.0238095 Monomial exponents: 6 0 1 0.000685871 3 0.0146391 3 0.00520833 6 0.0180884 6 0.013696 7 0.0177753 12 0.0178571 Exact 0.0178571 Monomial exponents: 5 1 1 0.000685871 3 0.00367584 3 0.00260417 6 0.00292335 6 0.00356867 7 0.00301713 12 0.00297619 Exact 0.00297619 Monomial exponents: 4 2 1 0.000685871 3 0.000975223 3 0.00260417 6 0.00114099 6 0.00113812 7 0.00114638 12 0.00119048 Exact 0.00119048 Monomial exponents: 3 3 1 0.000685871 3 0.00046082 3 0.00260417 6 0.00094955 6 0.000675154 7 0.000938524 12 0.000892857 Exact 0.000892857 Monomial exponents: 2 4 1 0.000685871 3 0.000975223 3 0.00260417 6 0.00114099 6 0.00113812 7 0.00114638 12 0.00119048 Exact 0.00119048 Monomial exponents: 1 5 1 0.000685871 3 0.00367584 3 0.00260417 6 0.00292335 6 0.00356867 7 0.00301713 12 0.00297619 Exact 0.00297619 Monomial exponents: 0 6 1 0.000685871 3 0.0146391 3 0.00520833 6 0.0180884 6 0.013696 7 0.0177753 12 0.0178571 Exact 0.0178571 Monomial exponents: 7 0 1 0.000228624 3 0.0097558 3 0.00260417 6 0.0141236 6 0.00904064 7 0.0136348 12 0.0138916 Exact 0.0138889 Monomial exponents: 6 1 1 0.000228624 3 0.00244163 3 0.00130208 6 0.00198238 6 0.00232767 7 0.00207021 12 0.00198275 Exact 0.00198413 Monomial exponents: 5 2 1 0.000228624 3 0.000619785 3 0.00130208 6 0.000583004 6 0.000688014 7 0.000601687 12 0.000661965 Exact 0.000661376 Monomial exponents: 4 3 1 0.000228624 3 0.000191115 3 0.00130208 6 0.000419591 6 0.000302212 7 0.000418121 12 0.000396629 Exact 0.000396825 Monomial exponents: 3 4 1 0.000228624 3 0.000191115 3 0.00130208 6 0.000419591 6 0.000302212 7 0.000418121 12 0.000396629 Exact 0.000396825 Monomial exponents: 2 5 1 0.000228624 3 0.000619785 3 0.00130208 6 0.000583004 6 0.000688014 7 0.000601687 12 0.000661965 Exact 0.000661376 Monomial exponents: 1 6 1 0.000228624 3 0.00244163 3 0.00130208 6 0.00198238 6 0.00232767 7 0.00207021 12 0.00198275 Exact 0.00198413 Monomial exponents: 0 7 1 0.000228624 3 0.0097558 3 0.00260417 6 0.0141236 6 0.00904064 7 0.0136348 12 0.0138916 Exact 0.0138889 TRIANGLE_FELIPPA_RULE_PRB Normal end of execution. 25 August 2014 11:55:21 PM