Novos Esquemas de Diferenças Finitas para a Equação de Helmholtz

Gustavo Benitez Alvarez; Helder da Fonseca Nunes

doi:10.35819/remat2024v10iespecialid7019

Autores/as

Gustavo Benitez Alvarez Universidade Federal Fluminense (UFF), Volta Redonda, RJ, Brasil https://orcid.org/0000-0002-2618-9513
Helder da Fonseca Nunes Universidade Federal Fluminense (UFF), Volta Redonda, RJ, Brasil https://orcid.org/0009-0005-9593-9241

DOI:

https://doi.org/10.35819/remat2024v10iespecialid7019

Palabras clave:

ecuación de Helmholtz, método de diferencias finitas, análisis de dispersión, polución del error, estabilización

Resumen

La ecuación escalar de Helmholtz describe los armónicos temporales de las ondas acústicas. Es bien conocido que los métodos de diferencias finitas y de elementos finitos presentan el efecto de polución del error para números de onda medios y altos. En este trabajo se analizan tres nuevos esquemas de diferencias finitas centradas de segundo orden de precisión en una y dos dimensiones. Estos nuevos esquemas son consistentes y se obtuvieron con nuevas aproximaciones sólo en el segundo término de la ecuación de Helmholtz. El análisis de dispersión, el comportamiento del error y los resultados numéricos muestran la eficacia de los Nuevos Esquemas 2 y 3. El Nuevo Esquema 3 es capaz de eliminar el efecto de polución del error en una dimensión y minimizar la dispersión de la onda plana en dos dimensiones.

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Biografía del autor/a

Gustavo Benitez Alvarez, Universidade Federal Fluminense (UFF), Volta Redonda, RJ, Brasil

http://lattes.cnpq.br/9571488360812994
Helder da Fonseca Nunes, Universidade Federal Fluminense (UFF), Volta Redonda, RJ, Brasil

http://lattes.cnpq.br/9801690867484750

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