High performance computing for partial differential equations
When representing realistic physical phenomena by partial differential equations (PDE), it is crucial to approximate the underlying physics correctly, to get precise results, and to efficiently use the computer architecture. Incorrect results can appear in incompressible Navier–Stokes or Stokes prob...
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| Veröffentlicht in: | Computers & fluids 2011-04, Vol.43 (1), p.68-73 |
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| creator | Gruber, R. Ahusborde, E. Azaïez, M. Keller, V. Latt, J. |
| description | When representing realistic physical phenomena by partial differential equations (PDE), it is crucial to approximate the underlying physics correctly, to get precise results, and to efficiently use the computer architecture. Incorrect results can appear in incompressible Navier–Stokes or Stokes problems when the numerical approach couples into spurious modes. In Maxwell or magnetohydrodynamic (MHD) equations the so-called spectrum pollution effect can occur, and the numerical solution does not stably converge to the physical one. Problems coming from a mesh that is not adapted to the underlying physical problem, or from an inadequate choice of the dependent and independent variables can lead to low precision. Efficiency of a code implementation can be improved by well adapting the parallel computer to the application. A new monitoring system enables to detect poor implementations, to find best suited resources to execute the job, and to adapt the processor frequency during. |
| doi_str_mv | 10.1016/j.compfluid.2010.07.001 |
| format | Article |
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Incorrect results can appear in incompressible Navier–Stokes or Stokes problems when the numerical approach couples into spurious modes. In Maxwell or magnetohydrodynamic (MHD) equations the so-called spectrum pollution effect can occur, and the numerical solution does not stably converge to the physical one. Problems coming from a mesh that is not adapted to the underlying physical problem, or from an inadequate choice of the dependent and independent variables can lead to low precision. Efficiency of a code implementation can be improved by well adapting the parallel computer to the application. 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Incorrect results can appear in incompressible Navier–Stokes or Stokes problems when the numerical approach couples into spurious modes. In Maxwell or magnetohydrodynamic (MHD) equations the so-called spectrum pollution effect can occur, and the numerical solution does not stably converge to the physical one. Problems coming from a mesh that is not adapted to the underlying physical problem, or from an inadequate choice of the dependent and independent variables can lead to low precision. Efficiency of a code implementation can be improved by well adapting the parallel computer to the application. A new monitoring system enables to detect poor implementations, to find best suited resources to execute the job, and to adapt the processor frequency during.</abstract><cop>Kidlington</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.compfluid.2010.07.001</doi><tpages>6</tpages><orcidid>https://orcid.org/0000-0003-0404-1152</orcidid></addata></record> |
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| subjects | Adaptive mesh Applied sciences Complexity function Computational fluid dynamics Computational methods in fluid dynamics Computer simulation COOL Electronic tubes, masers Electronics Exact sciences and technology Fluid dynamics Fluid flow Fundamental areas of phenomenology (including applications) Gyrotron simulation High performance computing methods Incompressibility condition Linear ideal MHD stability Magnetic confinement and equilibrium Mathematical analysis Mathematical models Mathematics Mesh density function Navier-Stokes equations Numerical Analysis Partial differential equations Physics Physics of gases, plasmas and electric discharges Physics of plasmas and electric discharges Processor frequency adaptation Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices Stellerator Stokes law (fluid mechanics) Stokes problem |
| title | High performance computing for partial differential equations |
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