Matches in SemOpenAlex for { <https://semopenalex.org/work/W76873415> ?p ?o ?g. }
Showing items 1 to 99 of
99
with 100 items per page.
- W76873415 abstract "In this dissertation we discuss the construction and convergence of high order structure preserving numerical methods for problems in Lagrangian mechanics. Specifically, we make use of the discrete mechanics framework to construct symplectic integrators which have convergence which is optimal, in a certain sense. We then demonstrate how this optimal convergence can be leveraged to construct integrators of arbitrarily high order or with geometric convergence. We further show how these methods can be used to construct continuous approximations to the dynamics of a Lagrangian system, and show that these approximations are also very high order and have excellent structure preserving properties. We discuss the formulation of symplectic integrators on both vector spaces and Lie groups, using a Galerkin construction to induce a variational integrator. We begin with the formulation for vector spaces, and then extend this construction to Lie groups through the use of a convenient coordinate chart. We provide the necessary conditions for optimal convergence for both the vector space and Lie group constructions, and demonstrate that many canonical systems automatically satisfy these conditions. We close with several numerical experiments demonstrating the predicted convergence, and discuss further extensions of this work" @default.
- W76873415 created "2016-06-24" @default.
- W76873415 creator A5079200124 @default.
- W76873415 date "2013-09-11" @default.
- W76873415 modified "2023-09-27" @default.
- W76873415 title "Convergence of Galerkin Variational Integrators for Vector Spaces and Lie Groups" @default.
- W76873415 cites W1495727713 @default.
- W76873415 cites W1593038947 @default.
- W76873415 cites W1805381866 @default.
- W76873415 cites W1978667419 @default.
- W76873415 cites W1989711829 @default.
- W76873415 cites W1992415540 @default.
- W76873415 cites W2009402935 @default.
- W76873415 cites W2033760732 @default.
- W76873415 cites W2037447641 @default.
- W76873415 cites W2039078443 @default.
- W76873415 cites W2040269741 @default.
- W76873415 cites W2071462623 @default.
- W76873415 cites W2071620266 @default.
- W76873415 cites W2072203191 @default.
- W76873415 cites W2096001350 @default.
- W76873415 cites W2098500157 @default.
- W76873415 cites W2112197455 @default.
- W76873415 cites W2119135605 @default.
- W76873415 cites W2119968067 @default.
- W76873415 cites W2128069584 @default.
- W76873415 cites W2158958880 @default.
- W76873415 cites W2170039048 @default.
- W76873415 cites W2171854205 @default.
- W76873415 cites W2519750562 @default.
- W76873415 cites W2799826576 @default.
- W76873415 cites W2947056241 @default.
- W76873415 cites W2963690049 @default.
- W76873415 cites W360270745 @default.
- W76873415 hasPublicationYear "2013" @default.
- W76873415 type Work @default.
- W76873415 sameAs 76873415 @default.
- W76873415 citedByCount "0" @default.
- W76873415 crossrefType "journal-article" @default.
- W76873415 hasAuthorship W76873415A5079200124 @default.
- W76873415 hasConcept C134306372 @default.
- W76873415 hasConcept C162324750 @default.
- W76873415 hasConcept C168619227 @default.
- W76873415 hasConcept C187915474 @default.
- W76873415 hasConcept C202444582 @default.
- W76873415 hasConcept C207646825 @default.
- W76873415 hasConcept C2776257435 @default.
- W76873415 hasConcept C2777303404 @default.
- W76873415 hasConcept C28826006 @default.
- W76873415 hasConcept C31258907 @default.
- W76873415 hasConcept C33923547 @default.
- W76873415 hasConcept C40265840 @default.
- W76873415 hasConcept C41008148 @default.
- W76873415 hasConcept C50522688 @default.
- W76873415 hasConcept C52154503 @default.
- W76873415 hasConcept C79518650 @default.
- W76873415 hasConceptScore W76873415C134306372 @default.
- W76873415 hasConceptScore W76873415C162324750 @default.
- W76873415 hasConceptScore W76873415C168619227 @default.
- W76873415 hasConceptScore W76873415C187915474 @default.
- W76873415 hasConceptScore W76873415C202444582 @default.
- W76873415 hasConceptScore W76873415C207646825 @default.
- W76873415 hasConceptScore W76873415C2776257435 @default.
- W76873415 hasConceptScore W76873415C2777303404 @default.
- W76873415 hasConceptScore W76873415C28826006 @default.
- W76873415 hasConceptScore W76873415C31258907 @default.
- W76873415 hasConceptScore W76873415C33923547 @default.
- W76873415 hasConceptScore W76873415C40265840 @default.
- W76873415 hasConceptScore W76873415C41008148 @default.
- W76873415 hasConceptScore W76873415C50522688 @default.
- W76873415 hasConceptScore W76873415C52154503 @default.
- W76873415 hasConceptScore W76873415C79518650 @default.
- W76873415 hasLocation W768734151 @default.
- W76873415 hasOpenAccess W76873415 @default.
- W76873415 hasPrimaryLocation W768734151 @default.
- W76873415 hasRelatedWork W2113926992 @default.
- W76873415 hasRelatedWork W2886900633 @default.
- W76873415 hasRelatedWork W2945000416 @default.
- W76873415 hasRelatedWork W2996011392 @default.
- W76873415 hasRelatedWork W2996020450 @default.
- W76873415 hasRelatedWork W2997905542 @default.
- W76873415 hasRelatedWork W3003679117 @default.
- W76873415 hasRelatedWork W3023826552 @default.
- W76873415 hasRelatedWork W3045374966 @default.
- W76873415 hasRelatedWork W3081588512 @default.
- W76873415 hasRelatedWork W3083752637 @default.
- W76873415 hasRelatedWork W3087948608 @default.
- W76873415 hasRelatedWork W3118377216 @default.
- W76873415 hasRelatedWork W3125920628 @default.
- W76873415 hasRelatedWork W3129347602 @default.
- W76873415 hasRelatedWork W3151915771 @default.
- W76873415 hasRelatedWork W3184681563 @default.
- W76873415 hasRelatedWork W3185918810 @default.
- W76873415 hasRelatedWork W3202482833 @default.
- W76873415 hasRelatedWork W3211129031 @default.
- W76873415 isParatext "false" @default.
- W76873415 isRetracted "false" @default.
- W76873415 magId "76873415" @default.
- W76873415 workType "article" @default.