A Tailored Finite Point Method for the Helmholtz Equation with High Wave Numbers in Heterogeneous Medium

Journal Home
Volume 39 - 2021
- Vol. 39, Issue 2 pp.159-310
- Vol. 39, Issue 1 pp.1-158
Volume 38 - 2020
- Vol. 38, Issue 6 pp.827-984
- Vol. 38, Issue 5 pp.683-826
- Vol. 38, Issue 4 pp.547-682
- Vol. 38, Issue 3 pp.395-546
- Vol. 38, Issue 2 pp.239-394
- Vol. 38, Issue 1 pp.1-238
Volume 37 - 2019
- Vol. 37, Issue 6 pp.739-936
- Vol. 37, Issue 5 pp.579-738
- Vol. 37, Issue 4 pp.437-578
- Vol. 37, Issue 3 pp.297-436
- Vol. 37, Issue 2 pp.151-296
- Vol. 37, Issue 1 pp.1-150
Volume 36 - 2018
- Vol. 36, Issue 6 pp.761-902
- Vol. 36, Issue 5 pp.627-760
- Vol. 36, Issue 4 pp.469-626
- Vol. 36, Issue 3 pp.331-468
- Vol. 36, Issue 2 pp.159-330
- Vol. 36, Issue 1 pp.1-158
Volume 35 - 2017
- Vol. 35, Issue 6 pp.693-838
- Vol. 35, Issue 5 pp.547-692
- Vol. 35, Issue 4 pp.381-546
- Vol. 35, Issue 3 pp.245-380
- Vol. 35, Issue 2 pp.121-244
- Vol. 35, Issue 1 pp.1-120
Volume 34 - 2016
- Vol. 34, Issue 6 pp.573-738
- Vol. 34, Issue 5 pp.451-572
- Vol. 34, Issue 4 pp.339-450
- Vol. 34, Issue 3 pp.223-338
- Vol. 34, Issue 2 pp.113-222
- Vol. 34, Issue 1 pp.1-112
Volume 33 - 2015
- Vol. 33, Issue 6 pp.557-684
- Vol. 33, Issue 5 pp.443-556
- Vol. 33, Issue 4 pp.341-442
- Vol. 33, Issue 3 pp.227-340
- Vol. 33, Issue 2 pp.113-226
- Vol. 33, Issue 1 pp.1-112
Volume 32 - 2014
- Vol. 32, Issue 6 pp.601-720
- Vol. 32, Issue 5 pp.491-600
- Vol. 32, Issue 4 pp.371-490
- Vol. 32, Issue 3 pp.215-370
- Vol. 32, Issue 2 pp.107-214
- Vol. 32, Issue 1 pp.1-106
Volume 31 - 2013
- Vol. 31, Issue 6 pp.549-662
- Vol. 31, Issue 5 pp.439-548
- Vol. 31, Issue 4 pp.335-438
- Vol. 31, Issue 3 pp.221-334
- Vol. 31, Issue 2 pp.107-220
- Vol. 31, Issue 1 pp.1-106
Volume 30 - 2012
- Vol. 30, Issue 6 pp.565-683
- Vol. 30, Issue 5 pp.449-564
- Vol. 30, Issue 4 pp.337-448
- Vol. 30, Issue 3 pp.223-336
- Vol. 30, Issue 2 pp.101-222
- Vol. 30, Issue 1 pp.1-100
Volume 29 - 2011
- Vol. 29, Issue 6 pp.605-719
- Vol. 29, Issue 5 pp.491-604
- Vol. 29, Issue 4 pp.367-490
- Vol. 29, Issue 3 pp.243-366
- Vol. 29, Issue 2 pp.131-242
- Vol. 29, Issue 1 pp.1-130
Volume 28 - 2010
- Vol. 28, Issue 6 pp.725-912
- Vol. 28, Issue 5 pp.569-724
- Vol. 28, Issue 4 pp.429-568
- Vol. 28, Issue 3 pp.289-428
- Vol. 28, Issue 2 pp.149-288
- Vol. 28, Issue 1 pp.1-148
Volume 27 - 2009
- Vol. 27, Issue 6 pp.677-834
- Vol. 27, Issue 5 pp.561-676
- Vol. 27, Issue 4 pp.425-560
- Vol. 27, Issue 2-3 pp.115-424
- Vol. 27, Issue 1 pp.1-114
Volume 26 - 2008
- Vol. 26, Issue 6 pp.767-892
- Vol. 26, Issue 5 pp.633-766
- Vol. 26, Issue 4 pp.471-632
- Vol. 26, Issue 3 pp.259-470
- Vol. 26, Issue 2 pp.123-258
- Vol. 26, Issue 1 pp.1-122
Volume 25 - 2007
- Vol. 25, Issue 6 pp.631-747
- Vol. 25, Issue 5 pp.497-630
- Vol. 25, Issue 4 pp.385-496
- Vol. 25, Issue 3 pp.243-384
- Vol. 25, Issue 2 pp.113-242
- Vol. 25, Issue 1 pp.1-112
Volume 24 - 2006
- Vol. 24, Issue 6 pp.675-790
- Vol. 24, Issue 5 pp.561-674
- Vol. 24, Issue 4 pp.451-560
- Vol. 24, Issue 3 pp.225-450
- Vol. 24, Issue 2 pp.113-224
- Vol. 24, Issue 1 pp.1-112
Volume 23 - 2005
- Vol. 23, Issue 6 pp.561-672
- Vol. 23, Issue 5 pp.449-560
- Vol. 23, Issue 4 pp.337-448
- Vol. 23, Issue 3 pp.225-336
- Vol. 23, Issue 2 pp.113-224
- Vol. 23, Issue 1 pp.1-112
Volume 22 - 2004
- Vol. 22, Issue 6 pp.777-920
- Vol. 22, Issue 5 pp.633-776
- Vol. 22, Issue 4 pp.489-632
- Vol. 22, Issue 3 pp.341-488
- Vol. 22, Issue 2 pp.145-340
- Vol. 22, Issue 1 pp.1-144
Volume 21 - 2003
- Vol. 21, Issue 6 pp.689-832
- Vol. 21, Issue 5 pp.545-688
- Vol. 21, Issue 4 pp.401-544
- Vol. 21, Issue 3 pp.257-400
- Vol. 21, Issue 2 pp.113-256
- Vol. 21, Issue 1 pp.1-112
Volume 20 - 2002
- Vol. 20, Issue 6 pp.561-672
- Vol. 20, Issue 5 pp.449-560
- Vol. 20, Issue 4 pp.337-448
- Vol. 20, Issue 3 pp.225-336
- Vol. 20, Issue 2 pp.113-224
- Vol. 20, Issue 1 pp.1-112
Volume 19 - 2001
- Vol. 19, Issue 6 pp.561-672
- Vol. 19, Issue 5 pp.449-560
- Vol. 19, Issue 4 pp.337-448
- Vol. 19, Issue 3 pp.225-336
- Vol. 19, Issue 2 pp.113-224
- Vol. 19, Issue 1 pp.1-112
Volume 18 - 2000
- Vol. 18, Issue 6 pp.561-672
- Vol. 18, Issue 5 pp.449-560
- Vol. 18, Issue 4 pp.337-448
- Vol. 18, Issue 3 pp.225-336
- Vol. 18, Issue 2 pp.113-224
- Vol. 18, Issue 1 pp.1-112
Volume 17 - 1999
- Vol. 17, Issue 6 pp.561-672
- Vol. 17, Issue 5 pp.449-560
- Vol. 17, Issue 4 pp.337-448
- Vol. 17, Issue 3 pp.225-336
- Vol. 17, Issue 2 pp.113-224
- Vol. 17, Issue 1 pp.1-112
Volume 16 - 1998
- Vol. 16, Issue 6 pp.481-576
- Vol. 16, Issue 5 pp.385-480
- Vol. 16, Issue 4 pp.289-384
- Vol. 16, Issue 3 pp.193-288
- Vol. 16, Issue 2 pp.97-192
- Vol. 16, Issue 1 pp.1-96
Volume 15 - 1997
- Vol. 15, Issue 4 pp.289-384
- Vol. 15, Issue 3 pp.193-288
- Vol. 15, Issue 2 pp.97-192
- Vol. 15, Issue 1 pp.1-96
Volume 14 - 1996
- Vol. 14, Issue 4 pp.291-386
- Vol. 14, Issue 3 pp.195-290
- Vol. 14, Issue 2 pp.99-194
- Vol. 14, Issue 1 pp.1-98
Volume 13 - 1995
- Vol. 13, Issue 4 pp.291-386
- Vol. 13, Issue 3 pp.193-290
- Vol. 13, Issue 2 pp.95-192
- Vol. 13, Issue 1 pp.1-94
Volume 12 - 1994
- Vol. 12, Issue 4 pp.291-386
- Vol. 12, Issue 3 pp.195-290
- Vol. 12, Issue 2 pp.98-194
- Vol. 12, Issue 1 pp.1-97
Volume 11 - 1993
- Vol. 11, Issue 4 pp.289-384
- Vol. 11, Issue 3 pp.193-288
- Vol. 11, Issue 2 pp.99-192
- Vol. 11, Issue 1 pp.1-98
Volume 10 - 1992
- Vol. 10, Issue 4 pp.291-387
- Vol. 10, Issue 3 pp.193-289
- Vol. 10, Issue 2 pp.97-193
- Vol. 10, Issue 1 pp.1-97
Volume 9 - 1991
- Vol. 9, Issue 4 pp.291-387
- Vol. 9, Issue 3 pp.193-289
- Vol. 9, Issue 2 pp.97-193
- Vol. 9, Issue 1 pp.1-96
Volume 8 - 1990
- Vol. 8, Issue 4 pp.289-381
- Vol. 8, Issue 3 pp.195-288
- Vol. 8, Issue 2 pp.99-194
- Vol. 8, Issue 1 pp.1-98
Volume 7 - 1989
- Vol. 7, Issue 4 pp.321-417
- Vol. 7, Issue 3 pp.227-320
- Vol. 7, Issue 2 pp.97-225
- Vol. 7, Issue 1 pp.1-96
Volume 6 - 1988
- Vol. 6, Issue 4 pp.293-382
- Vol. 6, Issue 3 pp.193-292
- Vol. 6, Issue 2 pp.97-192
- Vol. 6, Issue 1 pp.1-96
Volume 5 - 1987
- Vol. 5, Issue 4 pp.287-382
- Vol. 5, Issue 3 pp.191-286
- Vol. 5, Issue 2 pp.95-190
- Vol. 5, Issue 1 pp.1-94
Volume 4 - 1986
- Vol. 4, Issue 4 pp.289-382
- Vol. 4, Issue 3 pp.191-288
- Vol. 4, Issue 2 pp.97-190
- Vol. 4, Issue 1 pp.1-96
Volume 3 - 1985
- Vol. 3, Issue 4 pp.289-384
- Vol. 3, Issue 3 pp.193-288
- Vol. 3, Issue 2 pp.97-192
- Vol. 3, Issue 1 pp.1-96
Volume 2 - 1984
- Vol. 2, Issue 4 pp.287-381
- Vol. 2, Issue 3 pp.189-286
- Vol. 2, Issue 2 pp.93-188
- Vol. 2, Issue 1 pp.1-92
Volume 1 - 1983
- Vol. 1, Issue 4 pp.303-383
- Vol. 1, Issue 3 pp.195-302
- Vol. 1, Issue 2 pp.99-194
- Vol. 1, Issue 1 pp.1-98

Volume 26, Issue 5

Houde Han & Zhongyi Huang

DOI:

J. Comp. Math., 26 (2008), pp. 728-739

Published online: 2008-10

Preview Full PDF 107 1800

Export citation

Cited by

google scholar semantic scholar

Abstract

In this paper, we propose a tailored-finite-point method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, which allows us to obtain approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constant, we can get the exact solution with only one point in each subdomain. Our finite-point method has uniformly convergent rate with respect to wave number k in $L^2$-norm.

Keywords

Tailored finite point method Helmholtz equation Inhomogeneous media High frequency wave

AMS Subject Headings

65N99 74J05 74J40.

Email address

BibTex
RIS
TXT

@Article{JCM-26-728, author = {}, title = {A Tailored Finite Point Method for the Helmholtz Equation with High Wave Numbers in Heterogeneous Medium}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {5}, pages = {728--739}, abstract = { In this paper, we propose a tailored-finite-point method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, which allows us to obtain approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constant, we can get the exact solution with only one point in each subdomain. Our finite-point method has uniformly convergent rate with respect to wave number k in $L^2$-norm.}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8655.html} }

TY - JOUR T1 - A Tailored Finite Point Method for the Helmholtz Equation with High Wave Numbers in Heterogeneous Medium JO - Journal of Computational Mathematics VL - 5 SP - 728 EP - 739 PY - 2008 DA - 2008/10 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8655.html KW - Tailored finite point method KW - Helmholtz equation KW - Inhomogeneous media KW - High frequency wave AB - In this paper, we propose a tailored-finite-point method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, which allows us to obtain approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constant, we can get the exact solution with only one point in each subdomain. Our finite-point method has uniformly convergent rate with respect to wave number k in $L^2$-norm.

Houde Han & Zhongyi Huang. (1970). A Tailored Finite Point Method for the Helmholtz Equation with High Wave Numbers in Heterogeneous Medium. Journal of Computational Mathematics. 26 (5). 728-739. doi:

Copy to clipboard

BibteX RIS TXT

The citation has been copied to your clipboard