Matches in SemOpenAlex for { <https://semopenalex.org/work/W303312480> ?p ?o ?g. }
Showing items 1 to 89 of
89
with 100 items per page.
- W303312480 abstract "The modeling of problems with singularities and discontinuities, such as cracks in elastic media, is one of the most challenging problems in computational mechanics. The numerical solution of such problems necessitates sufficient resolution, which is very costly. In this work, model order reduction (MOR) techniques are developed for problems with singularities based on meshfree methods. Theoretical investigation on the performance of the proposed methods via error estimation, stability analysis, and complexity analysis is also carried out in this research.First, the full discrete model is constructed using enriched meshfree approximation to properly approximate singularities and discontinuities. This requires high order quadrature rules for accurate integration of enrichment functions and their derivative. An integrated singular basis function method (ISBFM) is introduced to circumvent this difficulty and the resulting ISBFM Galerkin formulation only integrates the enrichment functions on the boundaries away from the singularity point. This ISBFM Galerkin formulation also allows effective MOR procedures proposed in this work. Two MOR methods via projection of a discrete system obtained from the ISBFM Galerkin formulation have been proposed, the ISBFM-UR method based on a uniform projection and the ISBFM-DR method based on a decomposed projection of smooth and non-smooth DOF in order to retain the singular behavior of the full scale solution. Error estimation and stability analysis show that the reduced solution from ISBFM-DR can achieve a much-enhanced accuracy with slight increase of condition number compared to ISBFM-UR. While the stability analysis shows that the two MOR methods provide better conditioning than the full scale system, it also suggests that the conditioning of the ISBFM-DR method is compromised by its better accuracy compared to that of the ISBFM-UR method. Nevertheless, the complexity analysis shows that the ISBFM-DR method provides a better efficiency in addition to the enhanced accuracy compared to the ISBFM-UR method.The proposed MOR methods are applied Poisson problems with singularities and LEFM problems. The numerical tests validate the effectiveness of the MOR methods, and the numerical results on accuracy and stability of the proposed methods are shown to be in good agreement with the analytical predictions carried in this research." @default.
- W303312480 created "2016-06-24" @default.
- W303312480 creator A5027478901 @default.
- W303312480 date "2013-01-01" @default.
- W303312480 modified "2023-09-27" @default.
- W303312480 title "Model Order Reduction Methods for Meshfree Approximation of Problems with Singularities and Discontinuities" @default.
- W303312480 hasPublicationYear "2013" @default.
- W303312480 type Work @default.
- W303312480 sameAs 303312480 @default.
- W303312480 citedByCount "0" @default.
- W303312480 crossrefType "journal-article" @default.
- W303312480 hasAuthorship W303312480A5027478901 @default.
- W303312480 hasConcept C111335779 @default.
- W303312480 hasConcept C112972136 @default.
- W303312480 hasConcept C11413529 @default.
- W303312480 hasConcept C119599485 @default.
- W303312480 hasConcept C119857082 @default.
- W303312480 hasConcept C121332964 @default.
- W303312480 hasConcept C126255220 @default.
- W303312480 hasConcept C127413603 @default.
- W303312480 hasConcept C12843 @default.
- W303312480 hasConcept C134306372 @default.
- W303312480 hasConcept C135628077 @default.
- W303312480 hasConcept C15627037 @default.
- W303312480 hasConcept C16171025 @default.
- W303312480 hasConcept C162835735 @default.
- W303312480 hasConcept C186899397 @default.
- W303312480 hasConcept C202426404 @default.
- W303312480 hasConcept C2524010 @default.
- W303312480 hasConcept C28826006 @default.
- W303312480 hasConcept C33923547 @default.
- W303312480 hasConcept C41008148 @default.
- W303312480 hasConcept C57493831 @default.
- W303312480 hasConcept C5917680 @default.
- W303312480 hasConcept C62869609 @default.
- W303312480 hasConcept C65557600 @default.
- W303312480 hasConcept C97355855 @default.
- W303312480 hasConceptScore W303312480C111335779 @default.
- W303312480 hasConceptScore W303312480C112972136 @default.
- W303312480 hasConceptScore W303312480C11413529 @default.
- W303312480 hasConceptScore W303312480C119599485 @default.
- W303312480 hasConceptScore W303312480C119857082 @default.
- W303312480 hasConceptScore W303312480C121332964 @default.
- W303312480 hasConceptScore W303312480C126255220 @default.
- W303312480 hasConceptScore W303312480C127413603 @default.
- W303312480 hasConceptScore W303312480C12843 @default.
- W303312480 hasConceptScore W303312480C134306372 @default.
- W303312480 hasConceptScore W303312480C135628077 @default.
- W303312480 hasConceptScore W303312480C15627037 @default.
- W303312480 hasConceptScore W303312480C16171025 @default.
- W303312480 hasConceptScore W303312480C162835735 @default.
- W303312480 hasConceptScore W303312480C186899397 @default.
- W303312480 hasConceptScore W303312480C202426404 @default.
- W303312480 hasConceptScore W303312480C2524010 @default.
- W303312480 hasConceptScore W303312480C28826006 @default.
- W303312480 hasConceptScore W303312480C33923547 @default.
- W303312480 hasConceptScore W303312480C41008148 @default.
- W303312480 hasConceptScore W303312480C57493831 @default.
- W303312480 hasConceptScore W303312480C5917680 @default.
- W303312480 hasConceptScore W303312480C62869609 @default.
- W303312480 hasConceptScore W303312480C65557600 @default.
- W303312480 hasConceptScore W303312480C97355855 @default.
- W303312480 hasLocation W3033124801 @default.
- W303312480 hasOpenAccess W303312480 @default.
- W303312480 hasPrimaryLocation W3033124801 @default.
- W303312480 hasRelatedWork W1485042177 @default.
- W303312480 hasRelatedWork W156892634 @default.
- W303312480 hasRelatedWork W1993550263 @default.
- W303312480 hasRelatedWork W2042582613 @default.
- W303312480 hasRelatedWork W2043959457 @default.
- W303312480 hasRelatedWork W2055975268 @default.
- W303312480 hasRelatedWork W2078707745 @default.
- W303312480 hasRelatedWork W2085084320 @default.
- W303312480 hasRelatedWork W210730196 @default.
- W303312480 hasRelatedWork W2600441625 @default.
- W303312480 hasRelatedWork W2914154792 @default.
- W303312480 hasRelatedWork W3000470893 @default.
- W303312480 hasRelatedWork W3046834564 @default.
- W303312480 hasRelatedWork W3081838840 @default.
- W303312480 hasRelatedWork W3088350863 @default.
- W303312480 hasRelatedWork W3088619209 @default.
- W303312480 hasRelatedWork W3103543212 @default.
- W303312480 hasRelatedWork W3115393105 @default.
- W303312480 hasRelatedWork W3171592062 @default.
- W303312480 hasRelatedWork W2177828790 @default.
- W303312480 isParatext "false" @default.
- W303312480 isRetracted "false" @default.
- W303312480 magId "303312480" @default.
- W303312480 workType "article" @default.