LIBRARY ROUTINES FOR SPECTRAL METHODS. More...

Functions/Subroutines
subroutine	zwgl (Z, W, NP)
	Generate `NP` Gauss Legendre points `Z` and weights `W` associated with Jacobi polynomial \( P(N)(\alpha=0, \beta=0) \). The polynomial degree `N = NP-1`. More...

subroutine	zwgll (Z, W, NP)

subroutine	zwgj (Z, W, NP, ALPHA, BETA)

subroutine	zwgjd (Z, W, NP, ALPHA, BETA)

subroutine	zwglj (Z, W, NP, ALPHA, BETA)

subroutine	zwgljd (Z, W, NP, ALPHA, BETA)

real(kind=rp) function	endw1 (N, ALPHA, BETA)

real(kind=rp) function	endw2 (N, ALPHA, BETA)

real(kind=rp) function	gammaf (X)

real(kind=rp) function	pnormj (N, ALPHA, BETA)

subroutine	jacg (XJAC, NP, ALPHA, BETA)

subroutine	jacobf (POLY, PDER, POLYM1, PDERM1, POLYM2, PDERM2, N, ALP, BET, X)

real(kind=rp) function	hgj (II, Z, ZGJ, NP, ALPHA, BETA)

real(kind=rp) function	hgjd (II, Z, ZGJ, NP, ALPHA, BETA)

real(kind=rp) function	hglj (II, Z, ZGLJ, NP, ALPHA, BETA)

real(kind=rp) function	hgljd (I, Z, ZGLJ, NP, ALPHA, BETA)

subroutine	dgj (D, DT, Z, NZ, NZD, ALPHA, BETA)

subroutine	dgjd (D, DT, Z, NZ, NZD, ALPHA, BETA)

subroutine	dglj (D, DT, Z, NZ, NZD, ALPHA, BETA)

subroutine	dgljd (D, DT, Z, NZ, NZD, ALPHA, BETA)

subroutine	dgll (D, DT, Z, NZ, NZD)

real(kind=rp) function	hgll (I, Z, ZGLL, NZ)

real(kind=rp) function	hgl (I, Z, ZGL, NZ)

real(kind=rp) function	pnleg (Z, N)

real(kind=rp) function	pndleg (Z, N)

subroutine	dgllgl (D, DT, ZM1, ZM2, IM12, NZM1, NZM2, ND1, ND2)

subroutine	dgljgj (D, DT, ZGL, ZG, IGLG, NPGL, NPG, ND1, ND2, ALPHA, BETA)

subroutine	dgljgjd (D, DT, ZGL, ZG, IGLG, NPGL, NPG, ND1, ND2, ALPHA, BETA)

subroutine	iglm (I12, IT12, Z1, Z2, NZ1, NZ2, ND1, ND2)

subroutine	igllm (I12, IT12, Z1, Z2, NZ1, NZ2, ND1, ND2)

subroutine	igjm (I12, IT12, Z1, Z2, NZ1, NZ2, ND1, ND2, ALPHA, BETA)

subroutine	igljm (I12, IT12, Z1, Z2, NZ1, NZ2, ND1, ND2, ALPHA, BETA)

Detailed Description

LIBRARY ROUTINES FOR SPECTRAL METHODS.

March 1989

For questions, comments or suggestions, please contact:

Einar Malvin Ronquist Room 3-243 Department of Mechanical Engineering Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 0299 U.S.A.

Function/Subroutine Documentation

◆ dgj()

subroutine speclib::dgj	(	real(kind=rp), dimension(nzd,nzd)	D,
		real(kind=rp), dimension(nzd,nzd)	DT,
		real(kind=rp), dimension(1)	Z,
			NZ,
			NZD,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 689 of file speclib.f90.

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◆ dgjd()

subroutine speclib::dgjd	(	real(kind=rp), dimension(nzd,nzd)	D,
		real(kind=rp), dimension(nzd,nzd)	DT,
		real(kind=rp), dimension(1)	Z,
			NZ,
			NZD,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 733 of file speclib.f90.

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◆ dglj()

subroutine speclib::dglj	(	real(kind=rp), dimension(nzd,nzd)	D,
		real(kind=rp), dimension(nzd,nzd)	DT,
		real(kind=rp), dimension(1)	Z,
			NZ,
			NZD,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 772 of file speclib.f90.

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◆ dgljd()

subroutine speclib::dgljd	(	real(kind=rp), dimension(nzd,nzd)	D,
		real(kind=rp), dimension(nzd,nzd)	DT,
		real(kind=rp), dimension(1)	Z,
			NZ,
			NZD,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 816 of file speclib.f90.

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◆ dgljgj()

subroutine speclib::dgljgj	(	real(kind=rp), dimension(nd2,nd1)	D,
		real(kind=rp), dimension(nd1,nd2)	DT,
		real(kind=rp), dimension(nd1)	ZGL,
		real(kind=rp), dimension(nd2)	ZG,
		real(kind=rp), dimension(nd2,nd1)	IGLG,
			NPGL,
			NPG,
			ND1,
			ND2,
			ALPHA,
			BETA
	)

Definition at line 1042 of file speclib.f90.

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◆ dgljgjd()

subroutine speclib::dgljgjd	(	real(kind=rp), dimension(nd2,nd1)	D,
		real(kind=rp), dimension(nd1,nd2)	DT,
		real(kind=rp), dimension(nd1)	ZGL,
		real(kind=rp), dimension(nd2)	ZG,
		real(kind=rp), dimension(nd2,nd1)	IGLG,
			NPGL,
			NPG,
			ND1,
			ND2,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 1098 of file speclib.f90.

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◆ dgll()

subroutine speclib::dgll	(	real(kind=rp), dimension(nzd,nzd)	D,
		real(kind=rp), dimension(nzd,nzd)	DT,
		real(kind=rp), dimension(1)	Z,
			NZ,
			NZD
	)

Definition at line 863 of file speclib.f90.

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◆ dgllgl()

subroutine speclib::dgllgl	(	real(kind=rp), dimension(nd2,nd1)	D,
		real(kind=rp), dimension(nd1,nd2)	DT,
		real(kind=rp), dimension(nd1)	ZM1,
		real(kind=rp), dimension(nd2)	ZM2,
		real(kind=rp), dimension(nd2,nd1)	IM12,
			NZM1,
			NZM2,
			ND1,
			ND2
	)

Definition at line 1005 of file speclib.f90.

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◆ endw1()

real(kind=rp) function speclib::endw1	(		N,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 343 of file speclib.f90.

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◆ endw2()

real(kind=rp) function speclib::endw2	(		N,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 387 of file speclib.f90.

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◆ gammaf()

real(kind=rp) function speclib::gammaf ( real(kind=rp) X )

Definition at line 431 of file speclib.f90.

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◆ hgj()

real(kind=rp) function speclib::hgj	(		II,
		real(kind=rp)	Z,
		real(kind=rp), dimension(1)	ZGJ,
			NP,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 579 of file speclib.f90.

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◆ hgjd()

real(kind=rp) function speclib::hgjd	(		II,
		real(kind=rp)	Z,
		real(kind=rp), dimension(1)	ZGJ,
			NP,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 608 of file speclib.f90.

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◆ hgl()

real(kind=rp) function speclib::hgl	(		I,
		real(kind=rp)	Z,
		real(kind=rp), dimension(1)	ZGL,
			NZ
	)

Definition at line 922 of file speclib.f90.

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◆ hglj()

real(kind=rp) function speclib::hglj	(		II,
		real(kind=rp)	Z,
		real(kind=rp), dimension(1)	ZGLJ,
			NP,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 632 of file speclib.f90.

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◆ hgljd()

real(kind=rp) function speclib::hgljd	(		I,
		real(kind=rp)	Z,
		real(kind=rp), dimension(1)	ZGLJ,
			NP,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 661 of file speclib.f90.

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◆ hgll()

real(kind=rp) function speclib::hgll	(		I,
		real(kind=rp)	Z,
		real(kind=rp), dimension(1)	ZGLL,
			NZ
	)

Definition at line 900 of file speclib.f90.

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◆ igjm()

subroutine speclib::igjm	(	real(kind=rp), dimension(nd2,nd1)	I12,
		real(kind=rp), dimension(nd1,nd2)	IT12,
		real(kind=rp), dimension(nd1)	Z1,
		real(kind=rp), dimension(nd2)	Z2,
			NZ1,
			NZ2,
			ND1,
			ND2,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 1204 of file speclib.f90.

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◆ igljm()

subroutine speclib::igljm	(	real(kind=rp), dimension(nd2,nd1)	I12,
		real(kind=rp), dimension(nd1,nd2)	IT12,
		real(kind=rp), dimension(nd1)	Z1,
		real(kind=rp), dimension(nd2)	Z2,
			NZ1,
			NZ2,
			ND1,
			ND2,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 1231 of file speclib.f90.

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◆ igllm()

subroutine speclib::igllm	(	real(kind=rp), dimension(nd2,nd1)	I12,
		real(kind=rp), dimension(nd1,nd2)	IT12,
		real(kind=rp), dimension(nd1)	Z1,
		real(kind=rp), dimension(nd2)	Z2,
			NZ1,
			NZ2,
			ND1,
			ND2
	)

Definition at line 1178 of file speclib.f90.

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◆ iglm()

subroutine speclib::iglm	(	real(kind=rp), dimension(nd2,nd1)	I12,
		real(kind=rp), dimension(nd1,nd2)	IT12,
		real(kind=rp), dimension(nd1)	Z1,
		real(kind=rp), dimension(nd2)	Z2,
			NZ1,
			NZ2,
			ND1,
			ND2
	)

Definition at line 1152 of file speclib.f90.

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◆ jacg()

subroutine speclib::jacg	(	real(kind=rp), dimension(1)	XJAC,
			NP,
			ALPHA,
			BETA
	)

Definition at line 481 of file speclib.f90.

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◆ jacobf()

subroutine speclib::jacobf	(	POLY,
		PDER,
		POLYM1,
		PDERM1,
		POLYM2,
		PDERM2,
		N,
		ALP,
		BET,
		X
	)

Definition at line 539 of file speclib.f90.

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◆ pndleg()

real(kind=rp) function speclib::pndleg	(	real(kind=rp)	Z,
			N
	)

Definition at line 976 of file speclib.f90.

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◆ pnleg()

real(kind=rp) function speclib::pnleg	(	real(kind=rp)	Z,
			N
	)

Definition at line 941 of file speclib.f90.

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◆ pnormj()

real(kind=rp) function speclib::pnormj	(		N,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 455 of file speclib.f90.

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◆ zwgj()

subroutine speclib::zwgj	(	real(kind=rp), dimension(1)	Z,
		real(kind=rp), dimension(1)	W,
			NP,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 184 of file speclib.f90.

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◆ zwgjd()

subroutine speclib::zwgjd	(	real(kind=rp), dimension(1)	Z,
		real(kind=rp), dimension(1)	W,
			NP,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 215 of file speclib.f90.

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◆ zwgl()

subroutine speclib::zwgl	(	real(kind=rp), dimension(1)	Z,
		real(kind=rp), dimension(1)	W,
			NP
	)

Generate NP Gauss Legendre points Z and weights W associated with Jacobi polynomial \( P(N)(\alpha=0, \beta=0) \). The polynomial degree N = NP-1.

Parameters

Z	Quadrature points.
W	Quadrature weights.
NP	Number of quadrature points.

Definition at line 159 of file speclib.f90.

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◆ zwglj()

subroutine speclib::zwglj	(	real(kind=rp), dimension(1)	Z,
		real(kind=rp), dimension(1)	W,
			NP,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 267 of file speclib.f90.

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◆ zwgljd()

subroutine speclib::zwgljd	(	real(kind=rp), dimension(np)	Z,
		real(kind=rp), dimension(np)	W,
			NP,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 298 of file speclib.f90.

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◆ zwgll()

subroutine speclib::zwgll	(	real(kind=rp), dimension(1)	Z,
		real(kind=rp), dimension(1)	W,
			NP
	)

Definition at line 167 of file speclib.f90.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ dgj()

◆ dgjd()

◆ dglj()

◆ dgljd()

◆ dgljgj()

◆ dgljgjd()

◆ dgll()

◆ dgllgl()

◆ endw1()

◆ endw2()

◆ gammaf()

◆ hgj()

◆ hgjd()

◆ hgl()

◆ hglj()

◆ hgljd()

◆ hgll()

◆ igjm()

◆ igljm()

◆ igllm()

◆ iglm()

◆ jacg()

◆ jacobf()

◆ pndleg()

◆ pnleg()

◆ pnormj()

◆ zwgj()

◆ zwgjd()

◆ zwgl()

◆ zwglj()

◆ zwgljd()

◆ zwgll()