@Article{Xia2014a,
    author      = {Xia, Yidong and Luo, Hong and Frisbey, Megan and Nourgaliev, Robert},
    title       = {A set of parallel, implicit methods for a reconstructed discontinuous {Galerkin} method for compressible flows on 3D hybrid grids},
    doi         = {10.1016/j.compfluid.2014.01.023},
    issn        = {0045-7930},
    journal     = {Computers \& Fluids},
    keywords    = {Automatic differentiation, Discontinuous Galerkin, Hierarchical WENO reconstruction, Implicit methods, Parallel computing},
    month       = {July},
    pages       = {134--151},
    series      = {12th {USNCCM} mini-symposium of {High}-{Order} {Methods} for {Computational} {Fluid} {Dynamics} - {A} special issue dedicated to the 80th birthday of {Professor} {Antony} {Jameson}},
    volume      = {98},
    year        = {2014},
    abstract    = {A set of implicit methods are proposed for a third-order hierarchical WENO reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. An attractive feature in these methods are the application of the Jacobian matrix based on the P1 element approximation, resulting in a huge reduction of memory requirement compared with DG (P2). Also, three approaches --- analytical derivation, divided differencing, and automatic differentiation (AD) are presented to construct the Jacobian matrix respectively, where the AD approach shows the best robustness. A variety of compressible flow problems are computed to demonstrate the fast convergence property of the implemented flow solver. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results on complex geometries indicate that this low-storage implicit method can provide a viable and attractive DG solution for
                  complicated flows of practical importance.}
}

{"_id":"gvvXwhLR3atvzfRmo","bibbaseid":"xia-luo-frisbey-nourgaliev-asetofparallelimplicitmethodsforareconstructeddiscontinuousgalerkinmethodforcompressibleflowson3dhybridgrids-2014","author_short":["Xia, Y.","Luo, H.","Frisbey, M.","Nourgaliev, R."],"bibdata":{"bibtype":"article","type":"article","author":[{"propositions":[],"lastnames":["Xia"],"firstnames":["Yidong"],"suffixes":[]},{"propositions":[],"lastnames":["Luo"],"firstnames":["Hong"],"suffixes":[]},{"propositions":[],"lastnames":["Frisbey"],"firstnames":["Megan"],"suffixes":[]},{"propositions":[],"lastnames":["Nourgaliev"],"firstnames":["Robert"],"suffixes":[]}],"title":"A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids","doi":"10.1016/j.compfluid.2014.01.023","issn":"0045-7930","journal":"Computers & Fluids","keywords":"Automatic differentiation, Discontinuous Galerkin, Hierarchical WENO reconstruction, Implicit methods, Parallel computing","month":"July","pages":"134–151","series":"12th USNCCM mini-symposium of High-Order Methods for Computational Fluid Dynamics - A special issue dedicated to the 80th birthday of Professor Antony Jameson","volume":"98","year":"2014","abstract":"A set of implicit methods are proposed for a third-order hierarchical WENO reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. An attractive feature in these methods are the application of the Jacobian matrix based on the P1 element approximation, resulting in a huge reduction of memory requirement compared with DG (P2). Also, three approaches — analytical derivation, divided differencing, and automatic differentiation (AD) are presented to construct the Jacobian matrix respectively, where the AD approach shows the best robustness. A variety of compressible flow problems are computed to demonstrate the fast convergence property of the implemented flow solver. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results on complex geometries indicate that this low-storage implicit method can provide a viable and attractive DG solution for complicated flows of practical importance.","bibtex":"@Article{Xia2014a,\n author = {Xia, Yidong and Luo, Hong and Frisbey, Megan and Nourgaliev, Robert},\n title = {A set of parallel, implicit methods for a reconstructed discontinuous {Galerkin} method for compressible flows on 3D hybrid grids},\n doi = {10.1016/j.compfluid.2014.01.023},\n issn = {0045-7930},\n journal = {Computers \\& Fluids},\n keywords = {Automatic differentiation, Discontinuous Galerkin, Hierarchical WENO reconstruction, Implicit methods, Parallel computing},\n month = {July},\n pages = {134--151},\n series = {12th {USNCCM} mini-symposium of {High}-{Order} {Methods} for {Computational} {Fluid} {Dynamics} - {A} special issue dedicated to the 80th birthday of {Professor} {Antony} {Jameson}},\n volume = {98},\n year = {2014},\n abstract = {A set of implicit methods are proposed for a third-order hierarchical WENO reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. An attractive feature in these methods are the application of the Jacobian matrix based on the P1 element approximation, resulting in a huge reduction of memory requirement compared with DG (P2). Also, three approaches --- analytical derivation, divided differencing, and automatic differentiation (AD) are presented to construct the Jacobian matrix respectively, where the AD approach shows the best robustness. A variety of compressible flow problems are computed to demonstrate the fast convergence property of the implemented flow solver. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results on complex geometries indicate that this low-storage implicit method can provide a viable and attractive DG solution for\n complicated flows of practical importance.}\n}\n\n","author_short":["Xia, Y.","Luo, H.","Frisbey, M.","Nourgaliev, R."],"key":"Xia2014a","id":"Xia2014a","bibbaseid":"xia-luo-frisbey-nourgaliev-asetofparallelimplicitmethodsforareconstructeddiscontinuousgalerkinmethodforcompressibleflowson3dhybridgrids-2014","role":"author","urls":{},"keyword":["Automatic differentiation","Discontinuous Galerkin","Hierarchical WENO reconstruction","Implicit methods","Parallel computing"],"metadata":{"authorlinks":{}},"downloads":0,"html":""},"bibtype":"article","biburl":"https://raw.githubusercontent.com/mdolab/bib-file/refs/heads/master/mdolab.bib","dataSources":["qAPjQpsx8e9aJNrSa"],"keywords":["automatic differentiation","discontinuous galerkin","hierarchical weno reconstruction","implicit methods","parallel computing"],"search_terms":["set","parallel","implicit","methods","reconstructed","discontinuous","galerkin","method","compressible","flows","hybrid","grids","xia","luo","frisbey","nourgaliev"],"title":"A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids","year":2014}