Numerical anisotropy in finite differencing

Abstract Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In the multi-dimensional case, where the waves propagate in all directions, there is...
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Autor*in:	Sescu, Adrian [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	Finite Difference Scheme Advection Equation Numerical Dispersion Compact Scheme Helmholtz Equation

Übergeordnetes Werk:	Enthalten in: Advances in difference equations - [S.l.] : Springer International, 2004, 2015(2015), 1 vom: 16. Jan.
Übergeordnetes Werk:	volume:2015 ; year:2015 ; number:1 ; day:16 ; month:01

Links:	Volltext

DOI / URN:	10.1186/s13662-014-0343-0

Katalog-ID:	SPR032093691

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520			\|a Abstract Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In the multi-dimensional case, where the waves propagate in all directions, there is an additional specific error resulting from the discretization of spatial derivatives along the grid lines. Specifically, waves or wave packets in the multi-dimensional case propagate at different phase or group velocities, respectively, along different directions. A commonly used term for the aforementioned multi-dimensional discretization error is the numerical anisotropy or isotropy error. In this review, the numerical anisotropy is briefly described in the context of the wave equation in the multi-dimensional case. Then several important studies that were focused on optimizations of finite difference schemes with the objective of reducing the numerical anisotropy are discussed.
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650		4	\|a Helmholtz Equation \|7 (dpeaa)DE-He213
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allfields	10.1186/s13662-014-0343-0 doi (DE-627)SPR032093691 (SPR)s13662-014-0343-0-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Sescu, Adrian verfasserin aut Numerical anisotropy in finite differencing 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In the multi-dimensional case, where the waves propagate in all directions, there is an additional specific error resulting from the discretization of spatial derivatives along the grid lines. Specifically, waves or wave packets in the multi-dimensional case propagate at different phase or group velocities, respectively, along different directions. A commonly used term for the aforementioned multi-dimensional discretization error is the numerical anisotropy or isotropy error. In this review, the numerical anisotropy is briefly described in the context of the wave equation in the multi-dimensional case. Then several important studies that were focused on optimizations of finite difference schemes with the objective of reducing the numerical anisotropy are discussed. Finite Difference Scheme (dpeaa)DE-He213 Advection Equation (dpeaa)DE-He213 Numerical Dispersion (dpeaa)DE-He213 Compact Scheme (dpeaa)DE-He213 Helmholtz Equation (dpeaa)DE-He213 Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2015(2015), 1 vom: 16. Jan. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2015 year:2015 number:1 day:16 month:01 https://dx.doi.org/10.1186/s13662-014-0343-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2015 2015 1 16 01
spelling	10.1186/s13662-014-0343-0 doi (DE-627)SPR032093691 (SPR)s13662-014-0343-0-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Sescu, Adrian verfasserin aut Numerical anisotropy in finite differencing 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In the multi-dimensional case, where the waves propagate in all directions, there is an additional specific error resulting from the discretization of spatial derivatives along the grid lines. Specifically, waves or wave packets in the multi-dimensional case propagate at different phase or group velocities, respectively, along different directions. A commonly used term for the aforementioned multi-dimensional discretization error is the numerical anisotropy or isotropy error. In this review, the numerical anisotropy is briefly described in the context of the wave equation in the multi-dimensional case. Then several important studies that were focused on optimizations of finite difference schemes with the objective of reducing the numerical anisotropy are discussed. Finite Difference Scheme (dpeaa)DE-He213 Advection Equation (dpeaa)DE-He213 Numerical Dispersion (dpeaa)DE-He213 Compact Scheme (dpeaa)DE-He213 Helmholtz Equation (dpeaa)DE-He213 Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2015(2015), 1 vom: 16. Jan. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2015 year:2015 number:1 day:16 month:01 https://dx.doi.org/10.1186/s13662-014-0343-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2015 2015 1 16 01
allfields_unstemmed	10.1186/s13662-014-0343-0 doi (DE-627)SPR032093691 (SPR)s13662-014-0343-0-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Sescu, Adrian verfasserin aut Numerical anisotropy in finite differencing 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In the multi-dimensional case, where the waves propagate in all directions, there is an additional specific error resulting from the discretization of spatial derivatives along the grid lines. Specifically, waves or wave packets in the multi-dimensional case propagate at different phase or group velocities, respectively, along different directions. A commonly used term for the aforementioned multi-dimensional discretization error is the numerical anisotropy or isotropy error. In this review, the numerical anisotropy is briefly described in the context of the wave equation in the multi-dimensional case. Then several important studies that were focused on optimizations of finite difference schemes with the objective of reducing the numerical anisotropy are discussed. Finite Difference Scheme (dpeaa)DE-He213 Advection Equation (dpeaa)DE-He213 Numerical Dispersion (dpeaa)DE-He213 Compact Scheme (dpeaa)DE-He213 Helmholtz Equation (dpeaa)DE-He213 Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2015(2015), 1 vom: 16. Jan. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2015 year:2015 number:1 day:16 month:01 https://dx.doi.org/10.1186/s13662-014-0343-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2015 2015 1 16 01
allfieldsGer	10.1186/s13662-014-0343-0 doi (DE-627)SPR032093691 (SPR)s13662-014-0343-0-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Sescu, Adrian verfasserin aut Numerical anisotropy in finite differencing 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In the multi-dimensional case, where the waves propagate in all directions, there is an additional specific error resulting from the discretization of spatial derivatives along the grid lines. Specifically, waves or wave packets in the multi-dimensional case propagate at different phase or group velocities, respectively, along different directions. A commonly used term for the aforementioned multi-dimensional discretization error is the numerical anisotropy or isotropy error. In this review, the numerical anisotropy is briefly described in the context of the wave equation in the multi-dimensional case. Then several important studies that were focused on optimizations of finite difference schemes with the objective of reducing the numerical anisotropy are discussed. Finite Difference Scheme (dpeaa)DE-He213 Advection Equation (dpeaa)DE-He213 Numerical Dispersion (dpeaa)DE-He213 Compact Scheme (dpeaa)DE-He213 Helmholtz Equation (dpeaa)DE-He213 Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2015(2015), 1 vom: 16. Jan. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2015 year:2015 number:1 day:16 month:01 https://dx.doi.org/10.1186/s13662-014-0343-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2015 2015 1 16 01
allfieldsSound	10.1186/s13662-014-0343-0 doi (DE-627)SPR032093691 (SPR)s13662-014-0343-0-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Sescu, Adrian verfasserin aut Numerical anisotropy in finite differencing 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In the multi-dimensional case, where the waves propagate in all directions, there is an additional specific error resulting from the discretization of spatial derivatives along the grid lines. Specifically, waves or wave packets in the multi-dimensional case propagate at different phase or group velocities, respectively, along different directions. A commonly used term for the aforementioned multi-dimensional discretization error is the numerical anisotropy or isotropy error. In this review, the numerical anisotropy is briefly described in the context of the wave equation in the multi-dimensional case. Then several important studies that were focused on optimizations of finite difference schemes with the objective of reducing the numerical anisotropy are discussed. Finite Difference Scheme (dpeaa)DE-He213 Advection Equation (dpeaa)DE-He213 Numerical Dispersion (dpeaa)DE-He213 Compact Scheme (dpeaa)DE-He213 Helmholtz Equation (dpeaa)DE-He213 Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2015(2015), 1 vom: 16. Jan. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2015 year:2015 number:1 day:16 month:01 https://dx.doi.org/10.1186/s13662-014-0343-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2015 2015 1 16 01
language	English
source	Enthalten in Advances in difference equations 2015(2015), 1 vom: 16. Jan. volume:2015 year:2015 number:1 day:16 month:01
sourceStr	Enthalten in Advances in difference equations 2015(2015), 1 vom: 16. Jan. volume:2015 year:2015 number:1 day:16 month:01
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institution	findex.gbv.de
topic_facet	Finite Difference Scheme Advection Equation Numerical Dispersion Compact Scheme Helmholtz Equation
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container_title	Advances in difference equations
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author	Sescu, Adrian
spellingShingle	Sescu, Adrian ddc 510 bkl 31.49 misc Finite Difference Scheme misc Advection Equation misc Numerical Dispersion misc Compact Scheme misc Helmholtz Equation Numerical anisotropy in finite differencing
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topic_title	510 610 ASE 31.49 bkl Numerical anisotropy in finite differencing Finite Difference Scheme (dpeaa)DE-He213 Advection Equation (dpeaa)DE-He213 Numerical Dispersion (dpeaa)DE-He213 Compact Scheme (dpeaa)DE-He213 Helmholtz Equation (dpeaa)DE-He213
topic	ddc 510 bkl 31.49 misc Finite Difference Scheme misc Advection Equation misc Numerical Dispersion misc Compact Scheme misc Helmholtz Equation
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title	Numerical anisotropy in finite differencing
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title_sort	numerical anisotropy in finite differencing
title_auth	Numerical anisotropy in finite differencing
abstract	Abstract Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In the multi-dimensional case, where the waves propagate in all directions, there is an additional specific error resulting from the discretization of spatial derivatives along the grid lines. Specifically, waves or wave packets in the multi-dimensional case propagate at different phase or group velocities, respectively, along different directions. A commonly used term for the aforementioned multi-dimensional discretization error is the numerical anisotropy or isotropy error. In this review, the numerical anisotropy is briefly described in the context of the wave equation in the multi-dimensional case. Then several important studies that were focused on optimizations of finite difference schemes with the objective of reducing the numerical anisotropy are discussed.
abstractGer	Abstract Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In the multi-dimensional case, where the waves propagate in all directions, there is an additional specific error resulting from the discretization of spatial derivatives along the grid lines. Specifically, waves or wave packets in the multi-dimensional case propagate at different phase or group velocities, respectively, along different directions. A commonly used term for the aforementioned multi-dimensional discretization error is the numerical anisotropy or isotropy error. In this review, the numerical anisotropy is briefly described in the context of the wave equation in the multi-dimensional case. Then several important studies that were focused on optimizations of finite difference schemes with the objective of reducing the numerical anisotropy are discussed.
abstract_unstemmed	Abstract Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In the multi-dimensional case, where the waves propagate in all directions, there is an additional specific error resulting from the discretization of spatial derivatives along the grid lines. Specifically, waves or wave packets in the multi-dimensional case propagate at different phase or group velocities, respectively, along different directions. A commonly used term for the aforementioned multi-dimensional discretization error is the numerical anisotropy or isotropy error. In this review, the numerical anisotropy is briefly described in the context of the wave equation in the multi-dimensional case. Then several important studies that were focused on optimizations of finite difference schemes with the objective of reducing the numerical anisotropy are discussed.
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title_short	Numerical anisotropy in finite differencing
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Numerical anisotropy in finite differencing

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