Lines Matching refs:xi
46 const Real xi = p(0); in shape() local
56 return (1.-xi)/2.; in shape()
58 return (1.+xi)/2.; in shape()
68 return (1./4.)*pow<2>(1.-xi); in shape()
70 return (1./4.)*pow<2>(1.+xi); in shape()
72 return (1./2.)*(1.-xi)*(1.+xi); in shape()
82 return (1./8.)*pow<3>(1.-xi); in shape()
84 return (1./8.)*pow<3>(1.+xi); in shape()
86 return (3./8.)*(1.+xi)*pow<2>(1.-xi); in shape()
88 return (3./8.)*pow<2>(1.+xi)*(1.-xi); in shape()
98 return (1./16.)*pow<4>(1.-xi); in shape()
100 return (1./16.)*pow<4>(1.+xi); in shape()
102 return (1./ 4.)*(1.+xi)*pow<3>(1.-xi); in shape()
104 return (3./ 8.)*pow<2>(1.+xi)*pow<2>(1.-xi); in shape()
106 return (1./ 4.)*pow<3>(1.+xi)*(1.-xi); in shape()
117 return (1./32.)*pow<5>(1.-xi); in shape()
119 return (1./32.)*pow<5>(1.+xi); in shape()
121 return (5./32.)*(1.+xi)*pow<4>(1.-xi); in shape()
123 return (5./16.)*pow<2>(1.+xi)*pow<3>(1.-xi); in shape()
125 return (5./16.)*pow<3>(1.+xi)*pow<2>(1.-xi); in shape()
127 return (5./32.)*pow<4>(1.+xi)*(1.-xi); in shape()
138 return ( 1./64.)*pow<6>(1.-xi); in shape()
140 return ( 1./64.)*pow<6>(1.+xi); in shape()
142 return ( 3./32.)*(1.+xi)*pow<5>(1.-xi); in shape()
144 return (15./64.)*pow<2>(1.+xi)*pow<4>(1.-xi); in shape()
146 return ( 5./16.)*pow<3>(1.+xi)*pow<3>(1.-xi); in shape()
148 return (15./64.)*pow<4>(1.+xi)*pow<2>(1.-xi); in shape()
150 return ( 3./32.)*pow<5>(1.+xi)*(1.-xi); in shape()
177 return binomial_p_i * std::pow((1-xi)/2, p_order); in shape()
179 return binomial_p_i * std::pow((1+xi)/2, p_order); in shape()
182 return binomial_p_i * std::pow((1+xi)/2,n) in shape()
183 * std::pow((1-xi)/2,m); in shape()
232 const Real xi = p(0); in shape_deriv() local
255 return (xi-1.)*.5; in shape_deriv()
257 return (xi+1.)*.5; in shape_deriv()
259 return -xi; in shape_deriv()
269 return -0.375*pow<2>(1.-xi); in shape_deriv()
271 return 0.375*pow<2>(1.+xi); in shape_deriv()
273 return -0.375 -.75*xi +1.125*pow<2>(xi); in shape_deriv()
275 return 0.375 -.75*xi -1.125*pow<2>(xi); in shape_deriv()
285 return -0.25*pow<3>(1.-xi); in shape_deriv()
287 return 0.25*pow<3>(1.+xi); in shape_deriv()
289 return -0.5 +1.5*pow<2>(xi)-pow<3>(xi); in shape_deriv()
291 return 1.5*(pow<3>(xi)-xi); in shape_deriv()
293 return 0.5 -1.5*pow<2>(xi)-pow<3>(xi); in shape_deriv()
303 return -(5./32.)*pow<4>(xi-1.); in shape_deriv()
305 return (5./32.)*pow<4>(xi+1.); in shape_deriv()
307 return (5./32.)*pow<4>(1.-xi) -(5./8.)*(1.+xi)*pow<3>(1.-xi); in shape_deriv()
309 return (5./ 8.)*(1.+xi)*pow<3>(1.-xi) -(15./16.)*pow<2>(1.+xi)*pow<2>(1.-xi); in shape_deriv()
311 return -(5./ 8.)*pow<3>(1.+xi)*(1.-xi) +(15./16.)*pow<2>(1.+xi)*pow<2>(1.-xi); in shape_deriv()
313 return (5./ 8.)*pow<3>(1.+xi)*(1.-xi) -(5./32.)*pow<4>(1.+xi); in shape_deriv()
323 return -( 3./32.)*pow<5>(1.-xi); in shape_deriv()
325 return ( 3./32.)*pow<5>(1.+xi); in shape_deriv()
327 return ( 3./32.)*pow<5>(1.-xi)-(15./32.)*(1.+xi)*pow<4>(1.-xi); in shape_deriv()
329 return (15./32.)*(1.+xi)*pow<4>(1.-xi)-(15./16.)*pow<2>(1.+xi)*pow<3>(1.-xi); in shape_deriv()
331 return -(15./ 8.)*xi +(15./4.)*pow<3>(xi)-(15./8.)*pow<5>(xi); in shape_deriv()
333 return -(15./32.)*(1.-xi)*pow<4>(1.+xi)+(15./16.)*pow<2>(1.-xi)*pow<3>(1.+xi); in shape_deriv()
335 return (15./32.)*pow<4>(1.+xi)*(1.-xi)-(3./32.)*pow<5>(1.+xi); in shape_deriv()
362 return binomial_p_i * (-1./2.) * p_order * std::pow((1-xi)/2, p_order-1); in shape_deriv()
364 return binomial_p_i * ( 1./2.) * p_order * std::pow((1+xi)/2, p_order-1); in shape_deriv()
368 return binomial_p_i * (1./2. * n * std::pow((1+xi)/2,n-1) * std::pow((1-xi)/2,m) in shape_deriv()
369 - 1./2. * m * std::pow((1+xi)/2,n) * std::pow((1-xi)/2,m-1)); in shape_deriv()
422 const Real xi = p(0); in shape_second_deriv() local
457 return 0.75*(1.-xi); in shape_second_deriv()
459 return 0.75*(1.+xi); in shape_second_deriv()
461 return -.75 + 2.25*xi; in shape_second_deriv()
463 return -.75 - 2.25*xi; in shape_second_deriv()
473 return 0.75*pow<2>(1.-xi); in shape_second_deriv()
475 return 0.75*pow<2>(1.+xi); in shape_second_deriv()
477 return 3*(xi - pow<2>(xi)); in shape_second_deriv()
479 return 1.5*(3*pow<2>(xi)-1); in shape_second_deriv()
481 return -3*xi-3*pow<2>(xi); in shape_second_deriv()
491 return -(5./8.)*pow<3>(xi-1.); in shape_second_deriv()
493 return (5./8.)*pow<3>(xi+1.); in shape_second_deriv()
495 return -(5./4.)*pow<3>(1.-xi) + (15./8.)*(1.+xi)*pow<2>(1.-xi); in shape_second_deriv()
497 return -(15./ 4.)*(1.+xi)*pow<2>(1.-xi) + (5./ 8.)*pow<3>(1.-xi) in shape_second_deriv()
498 + (15./8.)*pow<2>(1.+xi)*(1.-xi); in shape_second_deriv()
500 return (5./ 8.)*pow<3>(1.+xi) - (15./ 4.)*pow<2>(1.+xi)*(1.-xi) in shape_second_deriv()
501 +(15./8.)*(1.+xi)*pow<2>(1.-xi); in shape_second_deriv()
503 return -(5./ 8.)*pow<3>(1.+xi) + (15./ 8.)*pow<2>(1.+xi)*(1.-xi) in shape_second_deriv()
504 -(5./8.)*pow<3>(1.+xi); in shape_second_deriv()
514 return ( 15./32.)*pow<4>(1.-xi); in shape_second_deriv()
516 return ( 15./32.)*pow<4>(1.+xi); in shape_second_deriv()
518 return -( 15./8.)*pow<4>(1.-xi) + in shape_second_deriv()
519 ( 15./8.)*(1.+xi)*pow<3>(1.-xi); in shape_second_deriv()
521 return -(15./4.)*(1.+xi)*pow<3>(1.-xi) in shape_second_deriv()
522 + (15./32.)*pow<4>(1.-xi) in shape_second_deriv()
523 + (45./16.)*pow<2>(1.+xi)*pow<2>(1.-xi); in shape_second_deriv()
525 return -(15./ 8.) +(45./4.)*pow<2>(xi) - (75./8.)*pow<4>(xi); in shape_second_deriv()
527 return -(15./4.)*(1.-xi)*pow<3>(1.+xi) in shape_second_deriv()
528 + (15./32.)*pow<4>(1.+xi) in shape_second_deriv()
529 + (45./16.)*pow<2>(1.-xi)*pow<2>(1.+xi); in shape_second_deriv()
531 return -(15./16.)*pow<4>(1.+xi) in shape_second_deriv()
532 + (15./8.)*pow<3>(1.+xi)*(1.-xi); in shape_second_deriv()
559 return binomial_p_i * (1./4.) * p_order * (p_order-1) * std::pow((1-xi)/2, p_order-2); in shape_second_deriv()
561 return binomial_p_i * (1./4.) * p_order * (p_order-1) * std::pow((1+xi)/2, p_order-2); in shape_second_deriv()
569 binomial_p_i * (-1./4. * m * std::pow((1-xi)/2,m-1)); in shape_second_deriv()
572 binomial_p_i * (-1./4. * n * m * std::pow((1+xi)/2,n-1) * std::pow((1-xi)/2,m-1) + in shape_second_deriv()
573 … 1./4. * n * (n-1) * std::pow((1+xi)/2,n-2) * std::pow((1-xi)/2,m)); in shape_second_deriv()
576 val += binomial_p_i * (-1./4. * n * std::pow((1+xi)/2,n-1)); in shape_second_deriv()
579 … binomial_p_i * (1./4. * m * (m-1) * std::pow((1+xi)/2,n) * std::pow((1-xi)/2,m-2) in shape_second_deriv()
580 … - 1./4. * m * n * std::pow((1+xi)/2,n-1) * std::pow((1-xi)/2,m-1)); in shape_second_deriv()