An Overlapping Preconditioner for 2D Virtual Problems Posed in H(rot) with Irregular Subdomains
dc.contributor.author | Calvo, Juan | |
dc.contributor.author | Herrera, César | |
dc.contributor.author | Sequeira, Filander | |
dc.date.accessioned | 2025-06-10T16:49:43Z | |
dc.date.available | 2025-06-10T16:49:43Z | |
dc.date.issued | 2022 | |
dc.description.abstract | Given a bounded polygonal domain Ω R2, we seek 𝒖 2 𝐻0 ¹rot;Ωº such that 𝑎¹𝒖 𝒗º := ∫ Ω ¹𝛼 rot 𝒖 rot 𝒗 ¸ 𝛽𝒖 𝒗º = ∫ Ω 𝒇 𝒗 8𝒗 2 𝐻0 ¹rot;Ωº (1) where rot 𝒖 := 𝜕𝑥1𝑢2 𝜕𝑥2𝑢1, 𝒇 2 »𝐿2 ¹Ωº¼2, and 𝛼 𝛽 2 𝐿1¹Ωº are positive functions that are uniformly bounded from below. The weak form (1) arises from implicit time integration of the eddy current model of Maxwell’s equation [5] and is considered in several studies; see, e.g., [1, 13]. We recall that 𝐻0 ¹rot;Ωº := { 𝒗 2 »𝐿2 ¹Ωº¼2 : rot 𝒗 2 𝐿2 ¹Ωº 𝒗 𝒕 = 0 on 𝜕 Ω } | |
dc.description.abstract | Dado un dominio poligonal acotado Ω R2, buscamos 𝒖 2 𝐻0 ¹rot;Ωº tal que 𝑎¹𝒖 𝒗º := ∫ Ω ¹𝛼 rot 𝒖 rot 𝒗 ¸ 𝛽𝒖 𝒗º = ∫ Ω 𝒇 𝒗 8𝒗 2 𝐻0 ¹rot;Ωº (1) donde rot 𝒖 : = 𝜕𝑥1𝑢2 𝜕𝑥2𝑢1, 𝒇 2 "𝐿2 ¹Ωº¼2, y 𝛼 𝛽 2 𝐿1¹Ωº son funciones positivas que están uniformemente acotadas desde abajo. La forma débil (1) surge de la integración temporal implícita del modelo de corrientes parásitas de la ecuación de Maxwell [5] y se considera en varios estudios; véase, por ejemplo, [1, 13]. Recordamos que 𝐻0 ¹rot;Ωº := { 𝒗 2 "𝐿2 ¹Ωº¼2 : rot 𝒗 2 𝐿2 ¹Ωº 𝒗 𝒕 = 0 en 𝜕 Ω } | |
dc.description.procedence | Escuela de Matemática | |
dc.description.sponsorship | Universidad Nacional, Costa Rica. | |
dc.identifier.uri | https://hdl.handle.net/11056/31539 | |
dc.language.iso | eng | |
dc.publisher | Springer | |
dc.rights | Acceso embargado | |
dc.rights | Attribution-NonCommercial-ShareAlike 4.0 International | en |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | |
dc.source | International Conference on Domain Decomposition Methods. 2022 | |
dc.subject | MATHEMATICS | |
dc.subject | EQUATIONS | |
dc.subject | POLYGONAL | |
dc.subject | GEOMETRY | |
dc.title | An Overlapping Preconditioner for 2D Virtual Problems Posed in H(rot) with Irregular Subdomains | |
dc.type | http://purl.org/coar/resource_type/c_8544 |
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