Searched for: subject:"filters"
(1 - 8 of 8)
document
Li, Xiaozhou (author), Ryan, J.K. (author), Kirby, Robert M. (author), Vuik, C. (author)
Smoothness-increasing accuracy-conserving (SIAC) filtering is an area of increasing interest because it can extract the “hidden accuracy” in discontinuous Galerkin (DG) solutions. It has been shown that by applying a SIAC filter to a DG solution, the accuracy order of the DG solution improves from order k+ 1 to order 2 k+ 1 for linear...
journal article 2019
document
Mirzaee, H. (author), King, J. (author), Ryan, J.K. (author), Kirby, R.M. (author)
The discontinuous Galerkin (DG) method has very quickly found utility in such diverse applications as computational solid mechanics, fluid mechanics, acoustics, and electromagnetics. The DG methodology merely requires weak constraints on the fluxes between elements. This feature provides a flexibility which is difficult to match with...
journal article 2013
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King, J. (author), Mirzaee, H. (author), Ryan, J.K. (author), Kirby, R.M. (author)
Smoothness-increasing accuracy-conserving (SIAC) filtering has demonstrated its effectiveness in raising the convergence rate of discontinuous Galerkin solutions from order k + 12 to order 2k + 1 for specific types of translation invariant meshes (Cockburn et al. in Math. Comput. 72:577–606, 2003; Curtis et al. in SIAM J. Sci. Comput. 30(1):272...
journal article 2012
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Mirzaee, H. (author), Li, L. (author), Ryan, J.K. (author), Kirby, R.M. (author)
Theoretically and computationally, it is possible to demonstrate that the order of accuracy of a discontinuous Galerkin (DG) solution for linear hyperbolic equations can be improved from order $k$+1 to 2$k$+1 through the use of smoothness-increasing accuracy-conserving (SIAC) filtering. However, it is a computationally complex task to perform...
journal article 2011
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Mirzaee, H. (author), Ryan, J.K. (author), Kirby, R.M. (author)
The discontinuous Galerkin (DG) methods provide a high-order extension of the finite volume method in much the same way as high-order or spectral/hp elements extend standard finite elements. However, lack of inter-element continuity is often contrary to the smoothness assumptions upon which many post-processing algorithms such as those used in...
journal article 2011
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Van Slingerland, P. (author), Ryan, J.K. (author), Vuik, C. (author)
Position-dependent smoothness-increasing accuracy-conserving (SIAC) filtering is a promising technique not only in improving the order of the numerical solution obtained by a discontinuous Galerkin (DG) method but also in increasing the smoothness of the field and improving the magnitude of the errors. This was initially established as an...
journal article 2011
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Mirzaee, H. (author), Ryan, J.K. (author), Kirby, R.M. (author)
The discontinuous Galerkin (DG) method continues to maintain heightened levels of interest within the simulation community because of the discretization flexibility it provides. Although one of the fundamental properties of the DG methodology and arguably its most powerful property is the ability to combine high-order discretizations on an...
journal article 2010
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Walfisch, D. (author), Ryan, J.K. (author), Kirby, R.M. (author), Haimes, R. (author)
The discontinuous Galerkin (DG) method continues to maintain heightened levels of interest within the simulation community because of the discretization flexibility it provides. One of the fundamental properties of the DG methodology and arguably its most powerful property is the ability to combine high-order discretizations on an inter-element...
journal article 2008
Searched for: subject:"filters"
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