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- 저자 : Yesom Jung (검색결과 3 건)
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Park, Yesom,Kim, Jeongho,Jung, Jinwook,Lee, Euntaek,Min, Chohong Elsevier 2018 Journal of computational physics Vol.356 No.-
<P><B>Abstract</B></P> <P>MILU preconditioning is known to be the optimal one among all the ILU-type preconditionings in solving the Poisson equation with Dirichlet boundary condition. It is optimal in the sense that it reduces the condition number from O ( <SUP> h − 2 </SUP> ) , which can be obtained from other ILU-type preconditioners, to O ( <SUP> h − 1 </SUP> ) . However, with Neumann boundary condition, the conventional MILU cannot be used since it is not invertible, and some MILU preconditionings achieved the order O ( <SUP> h − 1 </SUP> ) only in rectangular domains.</P> <P>In this article, we consider a standard finite volume method for solving the Poisson equation with Neumann boundary condition in general smooth domains, and introduce a new and efficient MILU preconditioning for the method in two dimensional general smooth domains. Our new MILU preconditioning achieved the order O ( <SUP> h − 1 </SUP> ) in all our empirical tests. In addition, in a circular domain with a fine grid, the CG method preconditioned with the proposed MILU runs about two times faster than the CG with ILU.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Some basic analyses on MILU preconditioning are presented to show the break-down of the conventional MILU. </LI> <LI> A mixture of MILU and ILU preconditioning is introduced and shown to be breakdown free. </LI> <LI> We introduce a novel conjecture for the MILU–ILU preconditioning. </LI> <LI> Numerical tests in two dimensions are provided to validate the conjecture. </LI> <LI> In three dimensions, numerical results do not follow the conjecture, exhibiting more than a simple translation. </LI> </UL> </P>
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JEONGHO KIM,JINWOOK JUNG,YESOM PARK,CHOHONG MIN,BYUNGJOON LEE 한국산업응용수학회 2019 Journal of the Korean Society for Industrial and A Vol.23 No.2
In this article, we introduce a finite difference method for solving the Navier-Stokes equations in rectangular domains. The method is proved to be energy stable and shown to be second-order accurate in several benchmark problems. Due to the guaranteed stability and the second order accuracy, the method can be a reliable tool in real-time simulations and physics-based animations with very dynamic fluid motion. We first discuss a simple convection equation, on which many standard explicit methods fail to be energy stable. Our method is an implicit Runge-Kutta method that preserves the energy for inviscid fluid and does not increase the energy for viscous fluid. Integration-by-parts in space is essential to achieve the energy stability, and we could achieve the integration-by-parts in discrete level by using the Marker-And-Cell configuration and central finite differences. The method, which is implicit and second-order accurate, extends our previous method [1] that was explicit and first- order accurate. It satisfies the energy stability and assumes rectangular domains. We acknowledge that the assumption on domains is restrictive, but the method is one of the few methods that are fully stable and second-order accurate.
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