lobatto.h File Reference

#include "common.h"

Go to the source code of this file.

Defines
#define	phi0(x)   (-2.0 * 1.22474487139158904909864203735)
	Kernel functions.
#define	phi1(x)   (-2.0 * 1.58113883008418966599944677222 * (x))
#define	phi2(x)   (-1.0 / 2.0 * 1.87082869338697069279187436616 * (5 * (x) * (x) - 1))
#define	phi3(x)   (-1.0 / 2.0 * 2.12132034355964257320253308631 * (7 * (x) * (x) - 3) * (x))
#define	phi4(x)   (-1.0 / 4.0 * 2.34520787991171477728281505677 * (21 * (x) * (x) * (x) * (x) - 14 * (x) * (x) + 1))
#define	phi5(x)   (-1.0 / 4.0 * 2.54950975679639241501411205451 * ((33 * (x) * (x) - 30) * (x) * (x) + 5) * (x))
#define	phi6(x)   (-1.0 / 32.0 * 2.73861278752583056728484891400 * (((429 * (x) * (x) - 495) * (x) * (x) + 135) * (x) * (x) - 5))
#define	phi7(x)   (-1.0 / 32.0 * 2.91547594742265023543707643877 * (((715 * (x) * (x) - 1001) * (x) * (x) + 385) * (x) * (x) - 35) * (x))
#define	phi8(x)   (-1.0 / 64.0 * 3.08220700148448822512509619073 * ((((2431 * (x) * (x) - 4004) * (x) * (x) + 2002) * (x) * (x) - 308) * (x) * (x) + 7))
#define	phi9(x)   (-1.0 / 64.0 * 3.24037034920393 * ((((4199 * (x) * (x) - 7956) * (x) * (x) + 4914) * (x) * (x) - 1092) * (x) * (x) + 63) * (x))
#define	phi0dx(x)   (0)
	Derivatives of kernel functions.
#define	phi1dx(x)   (-2.0 * 1.58113883008418966599944677222)
#define	phi2dx(x)   (-1.0 / 2.0 * 1.87082869338697069279187436616 * (10 * (x)))
#define	phi3dx(x)   (-1.0 / 2.0 * 2.12132034355964257320253308631 * (21.0*(x)*(x)-3.0))
#define	phi4dx(x)   (-1.0 / 4.0 * 2.34520787991171477728281505677 * ((84.0*(x)*(x)-28.0)*(x)))
#define	phi5dx(x)   (-1.0 / 4.0 * 2.54950975679639241501411205451 * ((165.0*(x)*(x)-90.0)*(x)*(x)+5.0))
#define	phi6dx(x)   (-1.0 / 32.0 * 2.73861278752583056728484891400 * (((2574.0*(x)*(x)-1980.0)*(x)*(x)+270.0)*(x)))
#define	phi7dx(x)   (-1.0 / 32.0 * 2.91547594742265023543707643877 * (((5005.0*(x)*(x)-5005.0)*(x)*(x)+1155.0)*(x)*(x)-35.0))
#define	phi8dx(x)   (-1.0 / 64.0 * 3.08220700148448822512509619073 * ((((19448.0*(x)*(x)-24024.0)*(x)*(x)+8008.0)*(x)*(x)-616.0)*(x)))
#define	phi9dx(x)   (-1.0 / 64.0 * 24037034920393 * ((((37791.0*(x)*(x)-55692.0)*(x)*(x)+24570.0)*(x)*(x)-3276.0)*(x)*(x)+63))
#define	legendre0(x)   (1.0)
#define	legendre1(x)   (x)
#define	legendre2(x)   (1.0 / 2.0 * (3 * (x) * (x) - 1))
#define	legendre3(x)   (1.0 / 2.0 * (5 * (x) * (x) - 3) * (x))
#define	legendre4(x)   (1.0 / 8.0 * ((35 * (x) * (x) - 30) * (x) * (x) + 3))
#define	legendre5(x)   (1.0 / 8.0 * ((63 * (x) * (x) - 70) * (x) * (x) + 15) * (x))
#define	legendre6(x)   (1.0 / 16.0 * (((231 * (x) * (x) - 315) * (x) * (x) + 105) * (x) * (x) - 5))
#define	legendre7(x)   (1.0 / 16.0 * (((429 * (x) * (x) - 693) * (x) * (x) + 315) * (x) * (x) - 35) * (x))
#define	legendre8(x)   (1.0 / 128.0 * ((((6435 * (x) * (x) - 12012) * (x) * (x) + 6930) * (x) * (x) - 1260) * (x) * (x) + 35))
#define	legendre9(x)   (1.0 / 128.0 * ((((12155 * (x) * (x) - 25740) * (x) * (x) + 18018) * (x) * (x) - 4620) * (x) * (x) + 315) * (x))
#define	legendre10(x)   (1.0 / 256.0 * (((((46189 * (x) * (x) - 109395) * (x) * (x) + 90090) * (x) * (x) - 30030) * (x) * (x) + 3465) * (x) * (x) - 63))
#define	legendre11(x)   (1.0 / 256.0 * (((((88179 * (x) * (x) - 230945) * (x) * (x) + 218790) * (x) * (x) - 90090) * (x) * (x) - 15015) * (x) * (x) - 693) * (x))
#define	legendre0x(x)   (0.0)
#define	legendre1x(x)   (1.0)
#define	legendre2x(x)   (3.0 * (x))
#define	legendre3x(x)   (15.0 / 2.0 * (x) * (x) - 3.0 / 2.0)
#define	legendre4x(x)   (5.0 / 2.0 * (x) * (7.0 * (x) * (x) - 3.0))
#define	legendre5x(x)   ((315.0 / 8.0 * (x) * (x) - 105.0 / 4.0) * (x) * (x) + 15.0 / 8.0)
#define	legendre6x(x)   (21.0 / 8.0 * (x) * ((33.0 * (x) * (x) - 30.0) * (x) * (x) + 5.0))
#define	legendre7x(x)   (((3003.0 / 16.0 * (x) * (x) - 3465.0 / 16.0) * (x) * (x) + 945.0 / 16.0) * (x) * (x) - 35.0 / 16.0)
#define	legendre8x(x)   (9.0 / 16.0 * (x) * (((715.0 * (x) * (x) - 1001.0) * (x) * (x) + 385.0) * (x) * (x) - 35.0))
#define	legendre9x(x)   ((((109395.0 / 128.0 * (x) * (x) - 45045.0 / 32.0) * (x) * (x) + 45045.0 / 64.0) * (x) * (x) - 3465.0 / 32.0) * (x) * (x) + 315.0 / 128.0)
#define	legendre10x(x)   (1.0 / 256.0 * ((((461890 * (x) * (x) - 875160) * (x) * (x) + 540540) * (x) * (x) - 120120) * (x) * (x) + 6930) * (x))
#define	legendre11x(x)   (1.0 / 256.0 * (((((969969 * (x) * (x) - 2078505) * (x) * (x) + 1531530) * (x) * (x) - 450450) * (x) * (x) + 45045) * (x) * (x) - 693))
#define	l0(x)   ((1.0 - (x)) * 0.5)
#define	l1(x)   ((1.0 + (x)) * 0.5)
#define	l0l1(x)   ((1.0 - (x)*(x)) * 0.25)
#define	l2(x)   (phi0(x) * l0l1(x))
#define	l3(x)   (phi1(x) * l0l1(x))
#define	l4(x)   (phi2(x) * l0l1(x))
#define	l5(x)   (phi3(x) * l0l1(x))
#define	l6(x)   (phi4(x) * l0l1(x))
#define	l7(x)   (phi5(x) * l0l1(x))
#define	l8(x)   (phi6(x) * l0l1(x))
#define	l9(x)   (phi7(x) * l0l1(x))
#define	l10(x)   (phi8(x) * l0l1(x))
#define	l11(x)   (phi9(x) * l0l1(x))
#define	dl0(x)   (-0.5)
#define	dl1(x)   (0.5)
#define	dl2(x)   (sqrt(3.0/2.0) * legendre1(x))
#define	dl3(x)   (sqrt(5.0/2.0) * legendre2(x))
#define	dl4(x)   (sqrt(7.0/2.0) * legendre3(x))
#define	dl5(x)   (sqrt(9.0/2.0) * legendre4(x))
#define	dl6(x)   (sqrt(11.0/2.0) * legendre5(x))
#define	dl7(x)   (sqrt(13.0/2.0) * legendre6(x))
#define	dl8(x)   (sqrt(15.0/2.0) * legendre7(x))
#define	dl9(x)   (sqrt(17.0/2.0) * legendre8(x))
#define	dl10(x)   (sqrt(19.0/2.0) * legendre9(x))
#define	dl11(x)   (sqrt(21.0/2.0) * legendre10(x))
Variables
shape_fn_1d_t	lobatto_fn_tab_1d []
shape_fn_1d_t	lobatto_der_tab_1d []
shape_fn_1d_t	legendre_fn_tab_1d []
shape_fn_1d_t	legendre_der_tab_1d []
int	lobatto_order_1d []
int	legendre_order_1d []

---

Define Documentation

#define dl0

(

x

)

(-0.5)

#define dl1

(

x

)

(0.5)

#define dl10

(

x

)

(sqrt(19.0/2.0) * legendre9(x))

#define dl11

(

x

)

(sqrt(21.0/2.0) * legendre10(x))

#define dl2

(

x

)

(sqrt(3.0/2.0) * legendre1(x))

#define dl3

(

x

)

(sqrt(5.0/2.0) * legendre2(x))

#define dl4

(

x

)

(sqrt(7.0/2.0) * legendre3(x))

#define dl5

(

x

)

(sqrt(9.0/2.0) * legendre4(x))

#define dl6

(

x

)

(sqrt(11.0/2.0) * legendre5(x))

#define dl7

(

x

)

(sqrt(13.0/2.0) * legendre6(x))

#define dl8

(

x

)

(sqrt(15.0/2.0) * legendre7(x))

#define dl9

(

x

)

(sqrt(17.0/2.0) * legendre8(x))

#define l0

(

x

)

((1.0 - (x)) * 0.5)

#define l0l1

(

x

)

((1.0 - (x)*(x)) * 0.25)

#define l1

(

x

)

((1.0 + (x)) * 0.5)

#define l10

(

x

)

(phi8(x) * l0l1(x))

#define l11

(

x

)

(phi9(x) * l0l1(x))

#define l2

(

x

)

(phi0(x) * l0l1(x))

#define l3

(

x

)

(phi1(x) * l0l1(x))

#define l4

(

x

)

(phi2(x) * l0l1(x))

#define l5

(

x

)

(phi3(x) * l0l1(x))

#define l6

(

x

)

(phi4(x) * l0l1(x))

#define l7

(

x

)

(phi5(x) * l0l1(x))

#define l8

(

x

)

(phi6(x) * l0l1(x))

#define l9

(

x

)

(phi7(x) * l0l1(x))

#define legendre0

(

x

)

(1.0)

#define legendre0x

(

x

)

(0.0)

#define legendre1

(

x

)

(x)

#define legendre10

(

x

)

(1.0 / 256.0 * (((((46189 * (x) * (x) - 109395) * (x) * (x) + 90090) * (x) * (x) - 30030) * (x) * (x) + 3465) * (x) * (x) - 63))

#define legendre10x

(

x

)

(1.0 / 256.0 * ((((461890 * (x) * (x) - 875160) * (x) * (x) + 540540) * (x) * (x) - 120120) * (x) * (x) + 6930) * (x))

#define legendre11

(

x

)

(1.0 / 256.0 * (((((88179 * (x) * (x) - 230945) * (x) * (x) + 218790) * (x) * (x) - 90090) * (x) * (x) - 15015) * (x) * (x) - 693) * (x))

#define legendre11x

(

x

)

(1.0 / 256.0 * (((((969969 * (x) * (x) - 2078505) * (x) * (x) + 1531530) * (x) * (x) - 450450) * (x) * (x) + 45045) * (x) * (x) - 693))

#define legendre1x

(

x

)

(1.0)

#define legendre2

(

x

)

(1.0 / 2.0 * (3 * (x) * (x) - 1))

#define legendre2x

(

x

)

(3.0 * (x))

#define legendre3

(

x

)

(1.0 / 2.0 * (5 * (x) * (x) - 3) * (x))

#define legendre3x

(

x

)

(15.0 / 2.0 * (x) * (x) - 3.0 / 2.0)

#define legendre4

(

x

)

(1.0 / 8.0 * ((35 * (x) * (x) - 30) * (x) * (x) + 3))

#define legendre4x

(

x

)

(5.0 / 2.0 * (x) * (7.0 * (x) * (x) - 3.0))

#define legendre5

(

x

)

(1.0 / 8.0 * ((63 * (x) * (x) - 70) * (x) * (x) + 15) * (x))

#define legendre5x

(

x

)

((315.0 / 8.0 * (x) * (x) - 105.0 / 4.0) * (x) * (x) + 15.0 / 8.0)

#define legendre6

(

x

)

(1.0 / 16.0 * (((231 * (x) * (x) - 315) * (x) * (x) + 105) * (x) * (x) - 5))

#define legendre6x

(

x

)

(21.0 / 8.0 * (x) * ((33.0 * (x) * (x) - 30.0) * (x) * (x) + 5.0))

#define legendre7

(

x

)

(1.0 / 16.0 * (((429 * (x) * (x) - 693) * (x) * (x) + 315) * (x) * (x) - 35) * (x))

#define legendre7x

(

x

)

(((3003.0 / 16.0 * (x) * (x) - 3465.0 / 16.0) * (x) * (x) + 945.0 / 16.0) * (x) * (x) - 35.0 / 16.0)

#define legendre8

(

x

)

(1.0 / 128.0 * ((((6435 * (x) * (x) - 12012) * (x) * (x) + 6930) * (x) * (x) - 1260) * (x) * (x) + 35))

#define legendre8x

(

x

)

(9.0 / 16.0 * (x) * (((715.0 * (x) * (x) - 1001.0) * (x) * (x) + 385.0) * (x) * (x) - 35.0))

#define legendre9

(

x

)

(1.0 / 128.0 * ((((12155 * (x) * (x) - 25740) * (x) * (x) + 18018) * (x) * (x) - 4620) * (x) * (x) + 315) * (x))

#define legendre9x

(

x

)

((((109395.0 / 128.0 * (x) * (x) - 45045.0 / 32.0) * (x) * (x) + 45045.0 / 64.0) * (x) * (x) - 3465.0 / 32.0) * (x) * (x) + 315.0 / 128.0)

#define phi0

(

x

)

(-2.0 * 1.22474487139158904909864203735)

Kernel functions.

#define phi0dx

(

x

)

(0)

Derivatives of kernel functions.

#define phi1

(

x

)

(-2.0 * 1.58113883008418966599944677222 * (x))

#define phi1dx

(

x

)

(-2.0 * 1.58113883008418966599944677222)

#define phi2

(

x

)

(-1.0 / 2.0 * 1.87082869338697069279187436616 * (5 * (x) * (x) - 1))

#define phi2dx

(

x

)

(-1.0 / 2.0 * 1.87082869338697069279187436616 * (10 * (x)))

#define phi3

(

x

)

(-1.0 / 2.0 * 2.12132034355964257320253308631 * (7 * (x) * (x) - 3) * (x))

#define phi3dx

(

x

)

(-1.0 / 2.0 * 2.12132034355964257320253308631 * (21.0*(x)*(x)-3.0))

#define phi4

(

x

)

(-1.0 / 4.0 * 2.34520787991171477728281505677 * (21 * (x) * (x) * (x) * (x) - 14 * (x) * (x) + 1))

#define phi4dx

(

x

)

(-1.0 / 4.0 * 2.34520787991171477728281505677 * ((84.0*(x)*(x)-28.0)*(x)))

#define phi5

(

x

)

(-1.0 / 4.0 * 2.54950975679639241501411205451 * ((33 * (x) * (x) - 30) * (x) * (x) + 5) * (x))

#define phi5dx

(

x

)

(-1.0 / 4.0 * 2.54950975679639241501411205451 * ((165.0*(x)*(x)-90.0)*(x)*(x)+5.0))

#define phi6

(

x

)

(-1.0 / 32.0 * 2.73861278752583056728484891400 * (((429 * (x) * (x) - 495) * (x) * (x) + 135) * (x) * (x) - 5))

#define phi6dx

(

x

)

(-1.0 / 32.0 * 2.73861278752583056728484891400 * (((2574.0*(x)*(x)-1980.0)*(x)*(x)+270.0)*(x)))

#define phi7

(

x

)

(-1.0 / 32.0 * 2.91547594742265023543707643877 * (((715 * (x) * (x) - 1001) * (x) * (x) + 385) * (x) * (x) - 35) * (x))

#define phi7dx

(

x

)

(-1.0 / 32.0 * 2.91547594742265023543707643877 * (((5005.0*(x)*(x)-5005.0)*(x)*(x)+1155.0)*(x)*(x)-35.0))

#define phi8

(

x

)

(-1.0 / 64.0 * 3.08220700148448822512509619073 * ((((2431 * (x) * (x) - 4004) * (x) * (x) + 2002) * (x) * (x) - 308) * (x) * (x) + 7))

#define phi8dx

(

x

)

(-1.0 / 64.0 * 3.08220700148448822512509619073 * ((((19448.0*(x)*(x)-24024.0)*(x)*(x)+8008.0)*(x)*(x)-616.0)*(x)))

#define phi9

(

x

)

(-1.0 / 64.0 * 3.24037034920393 * ((((4199 * (x) * (x) - 7956) * (x) * (x) + 4914) * (x) * (x) - 1092) * (x) * (x) + 63) * (x))

#define phi9dx

(

x

)

(-1.0 / 64.0 * 24037034920393 * ((((37791.0*(x)*(x)-55692.0)*(x)*(x)+24570.0)*(x)*(x)-3276.0)*(x)*(x)+63))

---

Variable Documentation

shape_fn_1d_t legendre_der_tab_1d[]

shape_fn_1d_t legendre_fn_tab_1d[]

int legendre_order_1d[]

shape_fn_1d_t lobatto_der_tab_1d[]

shape_fn_1d_t lobatto_fn_tab_1d[]

int lobatto_order_1d[]