On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation

We study the approximation properties of complex-valued polynomial Trefftz spaces for the ( d + 1 ) -dimensional linear time-dependent Schrödinger eq...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Gómez, Sergio [verfasserIn] Moiola, Andrea [verfasserIn] Perugia, Ilaria [verfasserIn] Stocker, Paul [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Schrödinger equation Ultra-weak formulation Discontinuous Galerkin method Extended Taylor polynomials Polynomial Trefftz space

Übergeordnetes Werk:	Enthalten in: Applied mathematics letters - Amsterdam [u.a.] : Elsevier Sci., 1988, 146
Übergeordnetes Werk:	volume:146

DOI / URN:	10.1016/j.aml.2023.108824

Katalog-ID:	ELV062702955

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100	1		\|a Gómez, Sergio \|e verfasserin \|0 (orcid)0000-0001-9156-5135 \|4 aut
245	1	0	\|a On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation
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520			\|a We study the approximation properties of complex-valued polynomial Trefftz spaces for the ( d + 1 ) -dimensional linear time-dependent Schrödinger equation. More precisely, we prove that for the space–time Trefftz discontinuous Galerkin variational formulation proposed by Gómez and Moiola (2022), the same h -convergence rates as for polynomials of degree p in ( d + 1 ) variables can be obtained in a mesh-dependent norm by using a space of Trefftz polynomials of anisotropic degree. For such a space, the dimension is equal to that of the space of polynomials of degree 2 p in d variables, and bases are easily constructed.
650		4	\|a Schrödinger equation
650		4	\|a Ultra-weak formulation
650		4	\|a Discontinuous Galerkin method
650		4	\|a Extended Taylor polynomials
650		4	\|a Polynomial Trefftz space
700	1		\|a Moiola, Andrea \|e verfasserin \|4 aut
700	1		\|a Perugia, Ilaria \|e verfasserin \|4 aut
700	1		\|a Stocker, Paul \|e verfasserin \|0 (orcid)0000-0001-5073-3366 \|4 aut
773	0	8	\|i Enthalten in \|t Applied mathematics letters \|d Amsterdam [u.a.] : Elsevier Sci., 1988 \|g 146 \|h Online-Ressource \|w (DE-627)320434222 \|w (DE-600)2004138-X \|w (DE-576)094085595 \|7 nnns
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936	b	k	\|a 31.80 \|j Angewandte Mathematik \|q VZ
951			\|a AR
952			\|d 146

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allfields	10.1016/j.aml.2023.108824 doi (DE-627)ELV062702955 (ELSEVIER)S0893-9659(23)00256-2 DE-627 ger DE-627 rda eng 510 VZ 31.80 bkl Gómez, Sergio verfasserin (orcid)0000-0001-9156-5135 aut On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the approximation properties of complex-valued polynomial Trefftz spaces for the ( d + 1 ) -dimensional linear time-dependent Schrödinger equation. More precisely, we prove that for the space–time Trefftz discontinuous Galerkin variational formulation proposed by Gómez and Moiola (2022), the same h -convergence rates as for polynomials of degree p in ( d + 1 ) variables can be obtained in a mesh-dependent norm by using a space of Trefftz polynomials of anisotropic degree. For such a space, the dimension is equal to that of the space of polynomials of degree 2 p in d variables, and bases are easily constructed. Schrödinger equation Ultra-weak formulation Discontinuous Galerkin method Extended Taylor polynomials Polynomial Trefftz space Moiola, Andrea verfasserin aut Perugia, Ilaria verfasserin aut Stocker, Paul verfasserin (orcid)0000-0001-5073-3366 aut Enthalten in Applied mathematics letters Amsterdam [u.a.] : Elsevier Sci., 1988 146 Online-Ressource (DE-627)320434222 (DE-600)2004138-X (DE-576)094085595 nnns volume:146 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2025 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2056 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 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_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.80 Angewandte Mathematik VZ AR 146
spelling	10.1016/j.aml.2023.108824 doi (DE-627)ELV062702955 (ELSEVIER)S0893-9659(23)00256-2 DE-627 ger DE-627 rda eng 510 VZ 31.80 bkl Gómez, Sergio verfasserin (orcid)0000-0001-9156-5135 aut On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the approximation properties of complex-valued polynomial Trefftz spaces for the ( d + 1 ) -dimensional linear time-dependent Schrödinger equation. More precisely, we prove that for the space–time Trefftz discontinuous Galerkin variational formulation proposed by Gómez and Moiola (2022), the same h -convergence rates as for polynomials of degree p in ( d + 1 ) variables can be obtained in a mesh-dependent norm by using a space of Trefftz polynomials of anisotropic degree. For such a space, the dimension is equal to that of the space of polynomials of degree 2 p in d variables, and bases are easily constructed. Schrödinger equation Ultra-weak formulation Discontinuous Galerkin method Extended Taylor polynomials Polynomial Trefftz space Moiola, Andrea verfasserin aut Perugia, Ilaria verfasserin aut Stocker, Paul verfasserin (orcid)0000-0001-5073-3366 aut Enthalten in Applied mathematics letters Amsterdam [u.a.] : Elsevier Sci., 1988 146 Online-Ressource (DE-627)320434222 (DE-600)2004138-X (DE-576)094085595 nnns volume:146 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2025 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2056 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 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_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.80 Angewandte Mathematik VZ AR 146
allfields_unstemmed	10.1016/j.aml.2023.108824 doi (DE-627)ELV062702955 (ELSEVIER)S0893-9659(23)00256-2 DE-627 ger DE-627 rda eng 510 VZ 31.80 bkl Gómez, Sergio verfasserin (orcid)0000-0001-9156-5135 aut On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the approximation properties of complex-valued polynomial Trefftz spaces for the ( d + 1 ) -dimensional linear time-dependent Schrödinger equation. More precisely, we prove that for the space–time Trefftz discontinuous Galerkin variational formulation proposed by Gómez and Moiola (2022), the same h -convergence rates as for polynomials of degree p in ( d + 1 ) variables can be obtained in a mesh-dependent norm by using a space of Trefftz polynomials of anisotropic degree. For such a space, the dimension is equal to that of the space of polynomials of degree 2 p in d variables, and bases are easily constructed. Schrödinger equation Ultra-weak formulation Discontinuous Galerkin method Extended Taylor polynomials Polynomial Trefftz space Moiola, Andrea verfasserin aut Perugia, Ilaria verfasserin aut Stocker, Paul verfasserin (orcid)0000-0001-5073-3366 aut Enthalten in Applied mathematics letters Amsterdam [u.a.] : Elsevier Sci., 1988 146 Online-Ressource (DE-627)320434222 (DE-600)2004138-X (DE-576)094085595 nnns volume:146 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2025 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2056 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 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_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.80 Angewandte Mathematik VZ AR 146
allfieldsGer	10.1016/j.aml.2023.108824 doi (DE-627)ELV062702955 (ELSEVIER)S0893-9659(23)00256-2 DE-627 ger DE-627 rda eng 510 VZ 31.80 bkl Gómez, Sergio verfasserin (orcid)0000-0001-9156-5135 aut On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the approximation properties of complex-valued polynomial Trefftz spaces for the ( d + 1 ) -dimensional linear time-dependent Schrödinger equation. More precisely, we prove that for the space–time Trefftz discontinuous Galerkin variational formulation proposed by Gómez and Moiola (2022), the same h -convergence rates as for polynomials of degree p in ( d + 1 ) variables can be obtained in a mesh-dependent norm by using a space of Trefftz polynomials of anisotropic degree. For such a space, the dimension is equal to that of the space of polynomials of degree 2 p in d variables, and bases are easily constructed. Schrödinger equation Ultra-weak formulation Discontinuous Galerkin method Extended Taylor polynomials Polynomial Trefftz space Moiola, Andrea verfasserin aut Perugia, Ilaria verfasserin aut Stocker, Paul verfasserin (orcid)0000-0001-5073-3366 aut Enthalten in Applied mathematics letters Amsterdam [u.a.] : Elsevier Sci., 1988 146 Online-Ressource (DE-627)320434222 (DE-600)2004138-X (DE-576)094085595 nnns volume:146 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2025 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2056 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 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_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.80 Angewandte Mathematik VZ AR 146
allfieldsSound	10.1016/j.aml.2023.108824 doi (DE-627)ELV062702955 (ELSEVIER)S0893-9659(23)00256-2 DE-627 ger DE-627 rda eng 510 VZ 31.80 bkl Gómez, Sergio verfasserin (orcid)0000-0001-9156-5135 aut On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the approximation properties of complex-valued polynomial Trefftz spaces for the ( d + 1 ) -dimensional linear time-dependent Schrödinger equation. More precisely, we prove that for the space–time Trefftz discontinuous Galerkin variational formulation proposed by Gómez and Moiola (2022), the same h -convergence rates as for polynomials of degree p in ( d + 1 ) variables can be obtained in a mesh-dependent norm by using a space of Trefftz polynomials of anisotropic degree. For such a space, the dimension is equal to that of the space of polynomials of degree 2 p in d variables, and bases are easily constructed. Schrödinger equation Ultra-weak formulation Discontinuous Galerkin method Extended Taylor polynomials Polynomial Trefftz space Moiola, Andrea verfasserin aut Perugia, Ilaria verfasserin aut Stocker, Paul verfasserin (orcid)0000-0001-5073-3366 aut Enthalten in Applied mathematics letters Amsterdam [u.a.] : Elsevier Sci., 1988 146 Online-Ressource (DE-627)320434222 (DE-600)2004138-X (DE-576)094085595 nnns volume:146 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2025 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2056 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 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_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.80 Angewandte Mathematik VZ AR 146
language	English
source	Enthalten in Applied mathematics letters 146 volume:146
sourceStr	Enthalten in Applied mathematics letters 146 volume:146
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bklname	Angewandte Mathematik
institution	findex.gbv.de
topic_facet	Schrödinger equation Ultra-weak formulation Discontinuous Galerkin method Extended Taylor polynomials Polynomial Trefftz space
dewey-raw	510
isfreeaccess_bool	false
container_title	Applied mathematics letters
authorswithroles_txt_mv	Gómez, Sergio @@aut@@ Moiola, Andrea @@aut@@ Perugia, Ilaria @@aut@@ Stocker, Paul @@aut@@
publishDateDaySort_date	2023-01-01T00:00:00Z
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author	Gómez, Sergio
spellingShingle	Gómez, Sergio ddc 510 bkl 31.80 misc Schrödinger equation misc Ultra-weak formulation misc Discontinuous Galerkin method misc Extended Taylor polynomials misc Polynomial Trefftz space On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation
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topic_title	510 VZ 31.80 bkl On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation Schrödinger equation Ultra-weak formulation Discontinuous Galerkin method Extended Taylor polynomials Polynomial Trefftz space
topic	ddc 510 bkl 31.80 misc Schrödinger equation misc Ultra-weak formulation misc Discontinuous Galerkin method misc Extended Taylor polynomials misc Polynomial Trefftz space
topic_unstemmed	ddc 510 bkl 31.80 misc Schrödinger equation misc Ultra-weak formulation misc Discontinuous Galerkin method misc Extended Taylor polynomials misc Polynomial Trefftz space
topic_browse	ddc 510 bkl 31.80 misc Schrödinger equation misc Ultra-weak formulation misc Discontinuous Galerkin method misc Extended Taylor polynomials misc Polynomial Trefftz space
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title	On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation
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title_full	On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation
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title_sort	on polynomial trefftz spaces for the linear time-dependent schrödinger equation
title_auth	On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation
abstract	We study the approximation properties of complex-valued polynomial Trefftz spaces for the ( d + 1 ) -dimensional linear time-dependent Schrödinger equation. More precisely, we prove that for the space–time Trefftz discontinuous Galerkin variational formulation proposed by Gómez and Moiola (2022), the same h -convergence rates as for polynomials of degree p in ( d + 1 ) variables can be obtained in a mesh-dependent norm by using a space of Trefftz polynomials of anisotropic degree. For such a space, the dimension is equal to that of the space of polynomials of degree 2 p in d variables, and bases are easily constructed.
abstractGer	We study the approximation properties of complex-valued polynomial Trefftz spaces for the ( d + 1 ) -dimensional linear time-dependent Schrödinger equation. More precisely, we prove that for the space–time Trefftz discontinuous Galerkin variational formulation proposed by Gómez and Moiola (2022), the same h -convergence rates as for polynomials of degree p in ( d + 1 ) variables can be obtained in a mesh-dependent norm by using a space of Trefftz polynomials of anisotropic degree. For such a space, the dimension is equal to that of the space of polynomials of degree 2 p in d variables, and bases are easily constructed.
abstract_unstemmed	We study the approximation properties of complex-valued polynomial Trefftz spaces for the ( d + 1 ) -dimensional linear time-dependent Schrödinger equation. More precisely, we prove that for the space–time Trefftz discontinuous Galerkin variational formulation proposed by Gómez and Moiola (2022), the same h -convergence rates as for polynomials of degree p in ( d + 1 ) variables can be obtained in a mesh-dependent norm by using a space of Trefftz polynomials of anisotropic degree. For such a space, the dimension is equal to that of the space of polynomials of degree 2 p in d variables, and bases are easily constructed.
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title_short	On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation
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up_date	2024-07-06T19:05:56.143Z
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On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation

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