{"id":377,"date":"2012-01-27T14:45:03","date_gmt":"2012-01-27T13:45:03","guid":{"rendered":"http:\/\/cio.zeus.umh.es\/2012\/02\/01\/stable-high-order-finite-difference-methods-based-on-non-uniform-grid-point-distributions.html"},"modified":"2012-01-27T14:45:03","modified_gmt":"2012-01-27T13:45:03","slug":"conferencia-prof-miguel-hermanns","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2012\/01\/27\/conferencia-prof-miguel-hermanns\/","title":{"rendered":"Conferencia Prof. Miguel Hermanns"},"content":{"rendered":"

T\u00edtulo<\/strong>: Stable high-order finite difference methods based on non-uniform grid point distributions
\nPonente<\/strong>: Miguel Hermanns
\nFecha<\/strong>: 30\/01\/2012 12:00h
\nLugar<\/strong>: Sala Seminarios, Edificio Torretamarit<\/p>\n

Title<\/strong>: Stable high-order finite difference methods based on non-uniform grid point distributions
\nSpeaker<\/strong>: Miguel Hermanns
\nDate<\/strong>: 30\/01\/2012 12:00h
\nLocation<\/strong>: Sala Seminarios, Edificio Torretamarit<\/p>\n

<\/h4>\n

\u00a0<\/p>\n

Resumen<\/h4>\n

When solving large and complex fluid dynamic problems, the use of high-order finite difference methods leads to reduced computational costs and memory requirements. However, high-order finite difference methods tend to become unstable in the presence of boundaries and the imposition of boundary conditions. Different theoretical approaches exist to overcome these limitations, like the GKS theory or the summation-by-parts rule. Although all these approaches have shown to indeed lead to finite difference methods of orders q = 4 to 8, the extension to even higher orders seems to be too cumbersome or unclear.
\nIn the present work a different approach is followed, namely the idea that the Runge phenomenon is behind the observed stability problems. By following the philosophy behind the Chebyshev interpolation theory, a non-uniform grid point distribution for piecewise polynomial interpolations of degree q < N is developed, being N+1 the number of grid points. The application of the developed methods to standard evolution problems like wave equation or convection-diffusion equation shows that the methods are stable for orders well beyond q = 10, recovering even the spectral accuracy in the limit q = N. Applications to stability analyses of fluid dynamic problems will also be presented, showing that the developed finite difference methods outperform in terms of accuracy and speed all the other existing finite difference methods and even the Chebyshev collocation method.<\/p>\n

Breve Bio<\/h4>\n

El profesor Miguel Hermanns es Doctor en Ingenier\u00eda Aeroespacial por la Universidad Polit\u00e9cnica de Madrid (2006) y obtuvo el grado de M\u00e1ster (2001) en Din\u00e1mica de Fluidos Experimental y Num\u00e9rica en el \u201cvon Karman Institute for Fluid Dynamics\u201d (B\u00e9lgica). Su trabajo investigador se ha centrado principalmente en modelizaci\u00f3n de procesos f\u00edsicos que involucran fluidos e intercambios de energ\u00eda, y en el desarrollo y aplicaciones de m\u00e9todos num\u00e9ricos de orden superior a todo tipo de problemas. En los \u00faltimos a\u00f1os tambi\u00e9n investiga en temas de eficiencia energ\u00e9tica en edificios.<\/h4>\n

Abstract<\/h4>\n

When solving large and complex fluid dynamic problems, the use of high-order finite difference methods leads to reduced computational costs and memory requirements. However, high-order finite difference methods tend to become unstable in the presence of boundaries and the imposition of boundary conditions. Different theoretical approaches exist to overcome these limitations, like the GKS theory or the summation-by-parts rule. Although all these approaches have shown to indeed lead to finite difference methods of orders q = 4 to 8, the extension to even higher orders seems to be too cumbersome or unclear.
\nIn the present work a different approach is followed, namely the idea that the Runge phenomenon is behind the observed stability problems. By following the philosophy behind the Chebyshev interpolation theory, a non-uniform grid point distribution for piecewise polynomial interpolations of degree q < N is developed, being N+1 the number of grid points. The application of the developed methods to standard evolution problems like wave equation or convection-diffusion equation shows that the methods are stable for orders well beyond q = 10, recovering even the spectral accuracy in the limit q = N. Applications to stability analyses of fluid dynamic problems will also be presented, showing that the developed finite difference methods outperform in terms of accuracy and speed all the other existing finite difference methods and even the Chebyshev collocation method.<\/p>\n

Brief Bio<\/h4>\n

El profesor Miguel Hermanns es Doctor en Ingenier\u00eda Aeroespacial por la Universidad Polit\u00e9cnica de Madrid (2006) y obtuvo el grado de M\u00e1ster (2001) en Din\u00e1mica de Fluidos Experimental y Num\u00e9rica en el \u201cvon Karman Institute for Fluid Dynamics\u201d (B\u00e9lgica). Su trabajo investigador se ha centrado principalmente en modelizaci\u00f3n de procesos f\u00edsicos que involucran fluidos e intercambios de energ\u00eda, y en el desarrollo y aplicaciones de m\u00e9todos num\u00e9ricos de orden superior a todo tipo de problemas. En los \u00faltimos a\u00f1os tambi\u00e9n investiga en temas de eficiencia energ\u00e9tica en edificios.<\/p>","protected":false},"excerpt":{"rendered":"

T\u00edtulo: Stable high-order finite difference methods based on non-uniform grid point distributions
\nPonente: Miguel Hermanns
\nFecha: 30\/01\/2012 12:00h
\nLugar: Sala Seminarios, Edificio Torretamarit
\nTitle: Stable high-order finite difference methods based on non-uniform grid point distributions
\nSpeaker: Miguel Hermanns
\nDate: 30\/01\/2012 12:00h
\nLocation: Sala Seminarios, Edificio Torretamarit<\/p>\n

\u00a0
\nResumen
\nWhen solving large and complex fluid dynamic problems, the use of high-order finite difference methods leads to […]<\/p>","protected":false},"author":3477,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[4,873],"tags":[],"_links":{"self":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/377"}],"collection":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/users\/3477"}],"replies":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/comments?post=377"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/377\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=377"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=377"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}