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并行谱数值方法/参考书目

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Allen, S.M.; Cahn, J.W. (1979), "A microscopic theory for antiphase boundary motion and its applications to antiphase domain coarsening", Acta Metallurgica, 27: 1085–1095


{AllCah79} S.M. Allen 和 J.W. Cahn, A microscopic theory for antiphase boundary motion and its applications to antiphase domain coarsening, Acta Metallurgica 27, 1085-1095, (1979).

Birkhoff, G; Rota, G.C. (1989). Ordinary Differential Equations (4 ed.). Wiley.

{BirRot89} G. Birkhoff 和 G.C. Rota, Ordinary Differential Equations (第 4 版), Wiley, (1989).

Blanes, S.; Casas, F.; Chartier, P.; Murua, A. "Splitting methods with complex coefficients for some classes of evolution equations". Mathematics of Computation.

{BlaCasChaMur12} S. Blanes, F. Casas, P. Chartier 和 A. Murua, Splitting methods with complex coefficients for some classes of evolution equations, Mathematics of Computation (即将出版) http://arxiv.org/abs/1102.1622

Bradie, B. (2006). A Friendly Introduction to Numerical Analysis. Pearson.

{Bra06} B. Bradie, A Friendly Introduction to Numerical Analysis, Pearson, (2006).

Boffetta, G.; Ecke, R.E. (2012). "Two-Dimensional Turbulence". Annual Review of Fluid Mechanics. 44: 427–451.

{BofEck12} G. Boffetta 和 R.E. Ecke, Two-Dimensional Turbulence, Annual Review of Fluid Mechanics 44, 427-451, (2012).

DiPrima, R.C. (2010). Elementary Differential Equations and Boundary Value Problems. Wiley. {{cite book}}: Cite has empty unknown parameter: |lnguage= (help)


{BoyDip10} W.E. Boyce 和 R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Wiley, (2010).

Boyd, J.P. (2001). Chebyshev and Fourier Spectral Methods. Dover.

{Boy01} J. P. Boyd, Chebyshev and Fourier Spectral Methods, Dover, (2001). http://www-personal.umich.edu/~jpboyd/

Canuto, C.; Hussaini, M.Y.; Quarteroni, A.; Zang, T.A. (2006). Spectral Methods: Fundamentals in Single Domains. Springer.

{CHQZ06} C. Canuto, M.Y. Hussaini, A. Quarteroni 和 T.A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer, (2006).

Canuto, C.; Hussaini, M.Y.; Quarteroni, A.; Zang, T.A. (2007). Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics. Springer.

{CHQZ07} C. Canuto, M.Y. Hussaini, A. Quarteroni 和 T.A. Zang, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics, Springer, (2007).

Cichowlas, C.; Brachet, M.-E. (2005). "Evolution of complex singularities in Kida-Pelz and Taylor-Green inviscid flows". Fluid Dynamics Research. 36: 239–248.

{CicBra05} C. Cichowlas 和 M.-E. Brachet, Evolution of complex singularities in Kida-Pelz and Taylor-Green inviscid flows, Fluid Dynamics Research 36, 239-248, (2005).

P., Rigge. "Performance of FORTRAN and C GPU Extensions for a Benchmark Suite of Fourier Pseudospectral Algorithms". Proceedings of the Symposium on Application Accelerators in High Performance computing. IEEE. http://arxiv.org/abs/1206.3215. 

{CloMuiRig12} B. Cloutier, B.K. Muite 和 P. Rigge, Performance of FORTRAN and C GPU Extensions for a Benchmark Suite of Fourier Pseudospectral Algorithms 即将出版的 Proceedings of the Symposium on Application Accelerators in High Performance computing (2012) http://arxiv.org/abs/1206.3215

Cooley, J.W.; Tukey, J.W. (1965). "An algorithm for the machine calculation of complex Fourier series". Mathematics of Computation. 19: 297–301.

{CooTuk65} J.W. Cooley 和 J.W. Tukey, An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation 19, 297-301, (1965).

Courant, R.; John, F. (1998). Introduction to Calculus and Analysis. Vol. I. Springer.

Courant, R.; John, F. (1999). Introduction to Calculus and Analysis. Vol. II. Springer.

{CouJoh98} R. Courant 和 F. John, Introduction to Calculus and Analysis I, II Springer (1998,1999)

Donninger, R.; Schlag, W. (2011). "Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation". Nonlinearity. 24: 2547–2562.

{DonSch11} R. Donninger 和 W. Schlag, Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation, Nonlinearity 24, 2547-2562, (2011).

Doering, C.R.; Gibbon, J.D. (1995). Applied Analysis of the Navier-Stokes Equations. Cambridge University Press.

{DoeGib95} C.R. Doering 和 J.D. Gibbon, Applied Analysis of the Navier-Stokes Equations, Cambridge University Press, (1995).

Shukla, P.K. (2009). "Nonlinear aspects of quantum plasma physics: Nanoplasmonics and nanostructures in dense plasmas". Plasma and Fusion Research: Review Articles. 4: 32.

{EliShu09} B. Eliasson 和 P. K. Shukla, Nonlinear aspects of quantum plasma physics: Nanoplasmonics and nanostructures in dense plasmas Plasma and Fusion Research: Review Articles, 4, 32 (2009).

Evans, L.C. (2010). Partial Differential Equations. American Mathematical Society.

{Eva10} L.C. Evans, Partial Differential Equations, American Mathematical Society, (2010).

Fornberg, B. (1977). "A numerical study of 2-D turbulence". Journal of Computational Physics. 25: 1–31.

{For77} B. Fornberg, A numerical study of 2-D turbulence, Journal of Computational Physics 25, 1-31, (1977).

Gallavotti, G. (2002). Foundations of Fluid Dynamics. Springer.

{Gal02} G. Gallavotti, Foundations of Fluid Dynamics, Springer, (2002).

http://www.math.rutgers.edu/~giovanni/glib.html#E 

Gottlieb, D.; Orszag, S.A. (1977). Numerical Analysis of Spectral Methods: Theory and Applications. SIAM.

{GotOrs77} D. Gottlieb 和 S.A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, (1977).

Grenier, W. (1994). 相对论量子力学. Springer.

{Gre94} W. Grenier, 相对论量子力学, Springer, (1994)

Skjellum, A. (1999). 使用 MPI. MIT 出版社.

{GroLusSkj99} W. Gropp, E. Lusk 和 A. Skjellum, 使用 MPI, MIT 出版社, (1999).

Gropp, W.; Lusk, E.; Thakur, R. (1999). 使用 MPI-2. MIT 出版社.

{GroLusTha99} W. Gropp, E. Lusk 和 R. Thakur, 使用 MPI-2, MIT 出版社, (1999).


Burrus, C.S. (1984). "高斯和快速傅里叶变换的历史". IEEE ASSP 杂志. 1 (4): 1421.

{HeiJohBur84} M.T. Heideman, D.H. Johnson 和 C.S. Burrus, 高斯和快速傅里叶变换的历史, IEEE ASSP 杂志 1(4), 1421, (1984).

Gottlieb, D. (2007). 时间相关问题的谱方法. 劍橋大學出版社.

{HesGotGot07} J.S. Hesthaven, S. Gottlieb 和 D. Gottlieb, 时间相关问题的谱方法, 劍橋大學出版社, (2007).

Hughes-Hallett, D. (2008). 微积分,单变量和多变量 (第 5 版). Wiley. {{cite book}}: 未知参数 |coauthors= 忽略 (|author= 建议) (帮助)

{HugEtAl08} D. Hughes-Hallett, A.M. Gleason, D.E. Flath, P.F. Lock, D.O. Lomen, D. Lovelock, W.G. MacCallum, D. Mumford, B. G. Osgood, D. Quinney, K. Rhea, J. Tecosky-Feldman, T.W. Tucker, 和 O.K. Bretscher, A. Iovita, W. Raskind, S.P. Gordon, A. Pasquale, J.B. Thrash, 微积分,单变量和多变量, 第 5 版. Wiley, (2008)

{{cite book}}: 空引用 (帮助)

{HolKarLieRis10} H. Holden, K.H. Karlsen, K.-A. Lie 和 N.H. Risebro, 偏微分方程的分解方法, 欧洲数学学会出版公司, 苏黎世, (2010).

Tao, T. (2011). "KdV 方程的算子分裂". 计算数学. 80: 821–846.

{HolKarRisTao11} H. Holden, K.H. Karlsen, N.H. Risebro 和 T. Tao, KdV 方程的算子分裂, 计算数学 80, 821-846, (2011).

Iserles, A. (2009). 微分方程数值分析入门. 劍橋大學出版社.

{Ise09} A. Iserles, 微分方程数值分析入门, 劍橋大學出版社, (2009).


{Joh12} R. Johnstone, 湍流直接数值模拟的改进缩放, HECTOR 分布式计算科学与工程报告, http://www.hector.ac.uk/cse/distributedcse/reports/ss3f-swt/

Klein, C. (2008). "低色散 Korteweg-De Vries 方程和非线性薛定谔方程的四阶时间步进". 数值分析电子交易. 29: 116–135.

{Kle08} C. Klein, 低色散 Korteweg-De Vries 方程和非线性薛定谔方程的四阶时间步进, 数值分析电子交易 29, 116-135, (2008).

Roidot, K. (2011). "Davey-Stewartson 系统中爆破的数值研究". {{cite journal}}: Cite journal requires |journal= (帮助)

{KleMuiRoi11} C. Klein, B.K. Muite 和 K. Roidot, Davey-Stewartson 系统中爆破的数值研究, http://arxiv.org/abs/1112.4043

Klein, C.; Roidot, K. (2011). "Kadomstev-Petviashvili 方程和 Davey-Stewartson 方程的四阶时间步进". SIAM 科学计算杂志. 33: 3333–3356.

{KleRoi11} C. Klein 和 K. Roidot, Kadomstev-Petviashvili 方程和 Davey-Stewartson 方程的四阶时间步进, SIAM 科学计算杂志 33, 3333-3356, (2011).

http://arxiv.org/abs/1108.3345 

Laizet, S.; Lamballais, E. (2009). "不可压缩流的高阶紧致格式:一种具有准谱精度的简单有效方法". 计算物理杂志. 238: 5989–6015.

{LaiLam09} S. Laizet 和 E. Lamballais, 不可压缩流的高阶紧致格式:一种具有准谱精度的简单有效方法, 计算物理杂志 228, 5989-6015, (2009).

Li, N. (2011). "Incompact3d:一个强大工具,可处理具有 个计算核心的湍流问题". 流体力学数值方法国际杂志. 67: 1735–1757.

{LaiLi11} S. Laizet 和 N. Li, Incompact3d:一个强大工具,可处理具有 个计算核心的湍流问题, 流体力学数值方法国际杂志 67, 1735-1757, (2011).

Landau, R.H. (1996). 量子力学 II. Wiley.

{Lan96} R. H. Landau, 量子力学 II, Wiley, (1996).

Lax, A. (1976). 应用与计算微积分. 第 1 卷. Springer.

{LaxBurLax76} P. Lax, S. Burstein 和 A. Lax, 应用与计算微积分,第 1 卷, Springer, (1976).

{LiLai10} N. Li 和 S. Laizet, 2DECOMP&FFT - 一个高度可扩展的二维分解库和 FFT 接口, 2010 年 Cray 用户组大会论文集.

http://web.archive.org/web/20130814233258/http://www.2decomp.org/pdf/17B-CUG2010-paper-Ning_LI.pdf 

Loss, M. (2003). 分析. 美国数学学会.

{LieLos03} E.H. Lieb 和 M. Loss,分析,美国数学学会,(2003).

Ponce, G. (2009). 非线性色散方程导论. 施普林格.

{LinPon09} F. Linares 和 G. Ponce,非线性色散方程导论,施普林格,(2009).

Wagenbreth, G. (2011). 高性能计算:编程与应用. CRC 出版社.

{LevWag11} J. Levesque 和 G. Wagenbreth,高性能计算:编程与应用,CRC 出版社,(2011).

Bertozzi, A.L. (2002). 涡度和不可压缩流. 剑桥大学出版社.

{MajBer02} A.J. Majda 和 A.L. Bertozzi,涡度和不可压缩流,剑桥大学出版社,(2002).

McLachlan, R.I.; Quispel, G.R.W. (2002). “分裂方法”. Acta Numerica. 11: 341–434.

{McLQui02} R.I. McLachlan 和 G.R.W. Quispel,分裂方法,Acta Numerica 11,341-434,(2002).

Cohen, M. (2011). 现代 Fortran 解释. 牛津大学出版社.

{MetReiCoh11} M. Metcalf, J. Reid 和 M. Cohen,现代 Fortran 解释,牛津大学出版社,(2011).

Schlag, W. (2011). 不变流形和色散哈密顿演化方程. 欧洲数学学会.

{NakSch11} K. Nakanishi 和 W. Schlag,不变流形和色散哈密顿演化方程,欧洲数学学会,(2011).

Olver, P.J. (2010). “色散量子化”. 美国数学月刊. 117: 599–610. {{cite journal}}: Cite has empty unknown parameter: |coauthors= (help)

{Olv10} P.J. Olver,色散量子化,美国数学月刊,117,599-610,(2010).

Shakiban, C. (2006). 应用线性代数. 普伦蒂斯·霍尔.

{OlvSha06} P.J. Olver 和 C. Shakiban,应用线性代数,普伦蒂斯·霍尔,(2006).

Orszag, S.A.; Patterson Jr., G.S. (1979). 物理评论快报. 28 (2): 76–79. {{cite journal}}: Missing or empty |title= (help)

{OrsPat72} S.A. Orszag 和 G.S. Patterson Jr.,三维均匀各向同性湍流的数值模拟,物理评论快报 28(2),76-79,(1972).

Peyret, R. (2002). 不可压缩粘性流的谱方法. 施普林格.

{Pey02} R. Peyret,不可压缩粘性流的谱方法,施普林格,(2002).

Rogers, R.C. (2004). 偏微分方程导论. 施普林格.

{RenRog04} R. Renardy 和 R.C. Rogers,偏微分方程导论,施普林格,(2004).

Shapiro, A (1993). “在三维非静力数值模型的验证测试中使用 Navier-Stokes 方程的精确解”. 每月天气评论. 121: 2420–2425. {{cite journal}}: Cite has empty unknown parameter: |coauthors= (help)

{Sha93} A. Shapiro 在三维非静力数值模型的验证测试中使用 Navier-Stokes 方程的精确解,每月天气评论 121,2420-2425,(1993).

Wang, L.-L. (2011). 谱方法:算法、分析与应用. 施普林格.

{SheTanWan11} J. Shen, T. Tang 和 L.-L. Wang,谱方法:算法、分析与应用,施普林格,(2011).

Sulem, P.L. (1999). 非线性薛定谔方程:自聚焦和波坍缩. 施普林格.

{SulSul99} C. Sulem 和 P.L. Sulem,非线性薛定谔方程:自聚焦和波坍缩,施普林格,(1999).

Temam, R. (2001). Navier-Stokes 方程 (第三版). 美国数学学会.

{Tem01} R. Temam,Navier-Stokes 方程,第三修订版,AMS,(2001).

{Tha08} M. Thalhammer,非线性薛定谔方程的时间分裂谱方法,未出版手稿,(2008).

http://techmath.uibk.ac.at/mecht/research/SpringSchool/manuscript_Thalhammer.pdf 

Trefethen, L.N. (2000). Matlab 中的谱方法. SIAM.

{Tre00} L. N. Trefethen,Matlab 中的谱方法,SIAM,(2000).

{TreEmb01} L. N. Trefethen 和 K. Embree (Ed.),(未完成)偏微分方程咖啡桌书。 未出版笔记,可在线获取

http://people.maths.ox.ac.uk/trefethen/pdectb.html 

Tritton, D.J. (1988). 物理流体动力学. 克拉伦登出版社.

{Tri88} D.J. Tritton,物理流体动力学,克拉伦登出版社,(1988).

{Uec09} H. Uecker,抛物线 PDE 和 Navier-Stokes 方程的谱方法简介,2009 年现代计算科学国际暑期学校讲义

http://www.staff.uni-oldenburg.de/hannes.uecker/hfweb-e.html 

Weideman, J.A.C.; Herbst, B.M. (1986). “非线性薛定谔方程解的步进分裂方法”. SIAM 数值分析杂志. SIAM. 23 (3): 485–507.

{WeiHer86} J.A.C. Weideman 和 B.M. Herbst,非线性薛定谔方程解的步进分裂方法,SIAM 数值分析杂志 23(3),485-507,(1986).

Yang, J. (2010). 可积和不可积系统中的非线性波. SIAM.

{Yan10} J. Yang,可积和不可积系统中的非线性波,SIAM,(2010).

{Yan06} L. Yang,Klein-Gordon-Schrödinger 方程的数值研究,新加坡国立大学硕士论文

http://scholarbank.nus.edu.sg/handle/10635/15515
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