Improvements in the discrete-dipole approximation method of computing scattering and absorption

Piotr J. Flatau

doi:10.1364/OL.22.001205

Improvements in the discrete-dipole approximation method of computing scattering and absorption

Piotr J. Flatau

Optics Letters
Vol. 22,
Issue 16,
pp. 1205-1207
(1997)
•https://doi.org/10.1364/OL.22.001205

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Piotr J. Flatau, "Improvements in the discrete-dipole approximation method of computing scattering and absorption," Opt. Lett. 22, 1205-1207 (1997)

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- Original Manuscript: April 14, 1997
- Published: August 15, 1997

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Abstract

Improvements in complex-conjugate gradient algorithms applied to the discrete-dipole approximation are reported. It is shown that computational time is reduced by use of the stabilized version of the biconjugate gratings algorithm, with diagonal left preconditioning.

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Method	$n = (1.33, 0)$	(2, 0)	(3, 0)	(5, 0)	(5, 0.0001)
CGNE	4.0(9)	4.9(24)	8.7(76)	*(540)	*(540)
CGNE(L)	3.3(7)	4.0(19)	7.8(67)	*(540)	*(540)
CGNE(R)	4.1(9)	4.9(24)	8.8(76)	*(540)	*(540)
CGNE(N) (L)	3.1(4)	4.1(13)	19.3(113)	*(540)	*(540)
CGNE(N) (R)	4.4(6)	7.7(25)	*(140)	*(540)	*(540)
CGNR	4.0(9)	4.7(23)	8.0(69)	*(540)	*(540)
CGNR(L)	3.3(7)	4.0(19)	5.9(50)	4.6(329)	3.5(330)
CGNR(R)	4.1(9)	4.7(23)	8.0(69)	*(540)	*(540)
QMR	3.7(6)	3.3(11)	3.3(19)	*(111)	*(78)
QMR(L)	2.6(4)	2.8(9)	2.7(15)	*(75)	*(92)
QMR(R)	3.8(6)	3.4(11)	3.4(19)	*(268)	*(540)
CG	1.4(6)	1.2(11)	1.2(20)	1.2(163)	1.1(213)
CG(L)	1.0(4)	1.0(9)	1.0(16)	1.0(138)	1.0(182)
CG(R)	1.4(6)	1.2(11)	1.2(20)	1.1(157)	1.2(213)
BiCG	2.3(6)	2.1(11)	*(140)	*(540)	*(540)
BiCG(L)	1.6(4)	1.8(9)	*(140)	*(540)	*(540)
BiCG(R)	2.4(6)	2.2(11)	*(140)	*(540)	*(540)
Bi-CGSTAB	1.8(4)	1.5(7)	1.5(13)	*(540)	*(540)
Bi-CGSTAB(L)	1.4(3)	1.3(6)	1.3(11)	4.0(281)	4.2(388)
Bi-CGSTAB(R)	1.8(4)	1.5(7)	1.6(13)	*(540)	*(540)
Bi-CGSTAB(N) (L)	1.9(2)	6.8(17)	14.9(65)	*(540)	*(540)
Bi-CGSTAB(N) (R)	2.1(2)	13.1(33)	27.9(122)	*(540)	*(540)
TFQMR	3.8(5)	3.4(9)	4.3(19)	*(540)	*(540)
TFQMR(L)	3.1(4)	3.1(8)	4.1(18)	*(540)	*(540)
TFQMR(R)	3.9(5)	3.5(9)	4.4(19)	*(540)	*(540)
CGS	1.7(4)	1.5(7)	1.4(12)	*(540)	*(540)
CGS(L)	1.4(3)	1.3(6)	1.2(10)	*(540)	*(540)
CGS(R)	1.8(4)	1.5(70)	1.4(12)	*(540)	*(540)

Method	$n = (1.33, 0)$	(1.33, 0.01)	(1.33, 1)	(2, 0)	(3, 0.0001)
CGNE	3.2(10)	3.2(10)	2.0(16)	4.5(33)	*(140)
CGNE (L)	2.7(8)	2.6(8)	1.7(13)	3.8(27)	*(140)
CGNE(R)	3.2(10)	3.2(10)	2.0(16)	4.6(33)	*(140)
CGNE(N) (L)	2.6(5)	2.6(5)	*(140)	*(140)	*(140)
CGNE(N) (R)	3.6(7)	3.6(7)	*(140)	*(140)	*(140)
CGNR	3.5(11)	3.5(11)	2.0(16)	4.3(32)	*(140)
CGNR(L)	2.7(8)	2.6(8)	1.7(13)	3.7(27)	*(140)
CGNR(R)	3.5(11)	3.5(11)	2.0(16)	4.4(32)	*(140)
QMR	*(47)	*(58)	*(25)	*(76)	*(50)
QMR(L)	5.3(12)	*(59)	*(21)	*(71)	*(39)
QMR(R)	*(52)	*(63)	*(22)	*(70)	*(37)
CG	1.3(8)	1.3(8)	*(140)	*(140)	*(140)
CG(L)	0.9(5)	0.9(5)	*(140)	*(140)	*(140)
CG(R)	1.3(8)	1.3(8)	*(140)	*(140)	*(140)
BiCG	*(140)	*(140)	*(140)	*(140)	*(140)
BiCG(L)	*(140)	*(140)	*(140)	*(140)	*(140)
BiCG(R)	*(140)	*(140)	*(140)	*(140)	*(140)
Bi-CGSTAB	1.3(4)	1.3(4)	1.2(10)	1.2(9)	1.1(24)
Bi-CGSTAB(L)	1.0(3)	1.0(3)	1.0(8)	1.0(7)	1.0(21)
Bi-CGSTAB(R)	1.3(4)	1.3(4)	1.2(10)	1.3(9)	1.1(24)
Bi-CGSTAB(N) (L)	1.4(2)	1.4(2)	1.5(6)	4.6(17)	*(140)
Bi-CGSTAB(N) (R)	1.5(2)	1.5(2)	1.6(6)	*(140)	*(140)
TFQMR	3.3(6)	3.3(6)	3.3(14)	3.4(13)	3.8(42)
TFQMR(L)	2.8(5)	2.8(5)	3.0(13)	3.0(11)	3.7(40)
TFQMR(R)	3.4(6)	3.4(6)	3.3(14)	3.4(13)	3.9(42)
CGS	1.3(4)	1.3(4)	1.3(11)	1.4(10)	1.6(34)
CGS(L)	1.0(3)	1.0(3)	1.2(10)	1.3(9)	1.1(23)
CGS(R)	1.3(4)	1.3(4)	1.3(11)	1.4(10)	1.6(33)

Method	$n = (1.33, 0)$	(2, 0)	(3, 0)	(5, 0)	(5, 0.0001)
CGNE	4.0(9)	4.9(24)	8.7(76)	*(540)	*(540)
CGNE(L)	3.3(7)	4.0(19)	7.8(67)	*(540)	*(540)
CGNE(R)	4.1(9)	4.9(24)	8.8(76)	*(540)	*(540)
CGNE(N) (L)	3.1(4)	4.1(13)	19.3(113)	*(540)	*(540)
CGNE(N) (R)	4.4(6)	7.7(25)	*(140)	*(540)	*(540)
CGNR	4.0(9)	4.7(23)	8.0(69)	*(540)	*(540)
CGNR(L)	3.3(7)	4.0(19)	5.9(50)	4.6(329)	3.5(330)
CGNR(R)	4.1(9)	4.7(23)	8.0(69)	*(540)	*(540)
QMR	3.7(6)	3.3(11)	3.3(19)	*(111)	*(78)
QMR(L)	2.6(4)	2.8(9)	2.7(15)	*(75)	*(92)
QMR(R)	3.8(6)	3.4(11)	3.4(19)	*(268)	*(540)
CG	1.4(6)	1.2(11)	1.2(20)	1.2(163)	1.1(213)
CG(L)	1.0(4)	1.0(9)	1.0(16)	1.0(138)	1.0(182)
CG(R)	1.4(6)	1.2(11)	1.2(20)	1.1(157)	1.2(213)
BiCG	2.3(6)	2.1(11)	*(140)	*(540)	*(540)
BiCG(L)	1.6(4)	1.8(9)	*(140)	*(540)	*(540)
BiCG(R)	2.4(6)	2.2(11)	*(140)	*(540)	*(540)
Bi-CGSTAB	1.8(4)	1.5(7)	1.5(13)	*(540)	*(540)
Bi-CGSTAB(L)	1.4(3)	1.3(6)	1.3(11)	4.0(281)	4.2(388)
Bi-CGSTAB(R)	1.8(4)	1.5(7)	1.6(13)	*(540)	*(540)
Bi-CGSTAB(N) (L)	1.9(2)	6.8(17)	14.9(65)	*(540)	*(540)
Bi-CGSTAB(N) (R)	2.1(2)	13.1(33)	27.9(122)	*(540)	*(540)
TFQMR	3.8(5)	3.4(9)	4.3(19)	*(540)	*(540)
TFQMR(L)	3.1(4)	3.1(8)	4.1(18)	*(540)	*(540)
TFQMR(R)	3.9(5)	3.5(9)	4.4(19)	*(540)	*(540)
CGS	1.7(4)	1.5(7)	1.4(12)	*(540)	*(540)
CGS(L)	1.4(3)	1.3(6)	1.2(10)	*(540)	*(540)
CGS(R)	1.8(4)	1.5(70)	1.4(12)	*(540)	*(540)

Method	$n = (1.33, 0)$	(1.33, 0.01)	(1.33, 1)	(2, 0)	(3, 0.0001)
CGNE	3.2(10)	3.2(10)	2.0(16)	4.5(33)	*(140)
CGNE (L)	2.7(8)	2.6(8)	1.7(13)	3.8(27)	*(140)
CGNE(R)	3.2(10)	3.2(10)	2.0(16)	4.6(33)	*(140)
CGNE(N) (L)	2.6(5)	2.6(5)	*(140)	*(140)	*(140)
CGNE(N) (R)	3.6(7)	3.6(7)	*(140)	*(140)	*(140)
CGNR	3.5(11)	3.5(11)	2.0(16)	4.3(32)	*(140)
CGNR(L)	2.7(8)	2.6(8)	1.7(13)	3.7(27)	*(140)
CGNR(R)	3.5(11)	3.5(11)	2.0(16)	4.4(32)	*(140)
QMR	*(47)	*(58)	*(25)	*(76)	*(50)
QMR(L)	5.3(12)	*(59)	*(21)	*(71)	*(39)
QMR(R)	*(52)	*(63)	*(22)	*(70)	*(37)
CG	1.3(8)	1.3(8)	*(140)	*(140)	*(140)
CG(L)	0.9(5)	0.9(5)	*(140)	*(140)	*(140)
CG(R)	1.3(8)	1.3(8)	*(140)	*(140)	*(140)
BiCG	*(140)	*(140)	*(140)	*(140)	*(140)
BiCG(L)	*(140)	*(140)	*(140)	*(140)	*(140)
BiCG(R)	*(140)	*(140)	*(140)	*(140)	*(140)
Bi-CGSTAB	1.3(4)	1.3(4)	1.2(10)	1.2(9)	1.1(24)
Bi-CGSTAB(L)	1.0(3)	1.0(3)	1.0(8)	1.0(7)	1.0(21)
Bi-CGSTAB(R)	1.3(4)	1.3(4)	1.2(10)	1.3(9)	1.1(24)
Bi-CGSTAB(N) (L)	1.4(2)	1.4(2)	1.5(6)	4.6(17)	*(140)
Bi-CGSTAB(N) (R)	1.5(2)	1.5(2)	1.6(6)	*(140)	*(140)
TFQMR	3.3(6)	3.3(6)	3.3(14)	3.4(13)	3.8(42)
TFQMR(L)	2.8(5)	2.8(5)	3.0(13)	3.0(11)	3.7(40)
TFQMR(R)	3.4(6)	3.4(6)	3.3(14)	3.4(13)	3.9(42)
CGS	1.3(4)	1.3(4)	1.3(11)	1.4(10)	1.6(34)
CGS(L)	1.0(3)	1.0(3)	1.2(10)	1.3(9)	1.1(23)
CGS(R)	1.3(4)	1.3(4)	1.3(11)	1.4(10)	1.6(33)

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