?? trefftz_method.cpp
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#include "vs.h"
#if defined(__TRANSCENDENTAL)
H1 cosh(const H1& a) { return (exp(a)+exp(-a))/2.0; }
#endif
int main() {
const double f_ = 1.0;
double weight[13] = {14.0/45.0, 64.0/45.0, 24.0/45.0, 64.0/45.0, 28.0/45.0,
64.0/45.0, 24.0/45.0, 64.0/45.0, 28.0/45.0,
64.0/45.0, 24.0/45.0, 64.0/45.0, 14.0/45.0};
Quadrature qp(weight, 0.0, 1.0, 13);
J d_l(1.0/12.0); // per normalized length
H1 X = INTEGRABLE_VECTOR_OF_TANGENT_BUNDLE( "int, int, Quadrature", 2, 2, qp),
phi = INTEGRABLE_VECTOR_OF_TANGENT_BUNDLE( "int, int, Quadrature", 2, 2, qp),
x, y; x &= X[0]; y &= X[1];
((H0)x) = 1.0; d(y) = 0.0;
H0 v_bar = f_/4.0 *(((H0)x).pow(2)+((H0)y).pow(2));
#if defined(__TRANSCENDENTAL)
const double PI = 3.141592654;
phi[0] = cos(PI/2.0*x)*cosh(PI/2.0*y) + cos(PI/2.0*y)*cosh(PI/2.0*x);
phi[1] = cos(3.0*PI/2.0*x)*cosh(3.0*PI/2.0*y) + cos(3.0*PI/2.0*y)*cosh(3.0*PI/2.0*x);
#else
phi[0] = x.pow(4) - 6.0*x.pow(2)*y.pow(2) + y.pow(4);
phi[1] = x.pow(8) -28.0*x.pow(6)*y.pow(2)+70.0*x.pow(4)*y.pow(4)
-28.0*x.pow(2)*y.pow(6)+y.pow(8);
#endif
H0 dphi_dx = d(phi)(0);
C0 M = dphi_dx % ((H0)phi) | d_l,
b = dphi_dx * v_bar | d_l;
C0 c = b / M;
cout << c << endl;
C0 k = -((- v_bar + ((H0)phi)*c) | d_l);
cout << k << endl;
return 0;
}
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