Papers by Chen-Song Zhang
We confirm numerically that the Johnson-Segalman model is able to reproduce the continual oscilla... more We confirm numerically that the Johnson-Segalman model is able to reproduce the continual oscillations of the falling sphere observed in some viscoelastic models. The empirical choice of parameters used in the Johnson-Segalman model is from the ones that show the non-monotone stress-strain relation of the steady shear flows of the model. The carefully chosen parameters yield continual, self-sustaining, (ir)regular and periodic oscillations of the speed for the falling sphere through the Johnson-Segalman fluids. In particular, our simulations reproduce the phenomena: the falling sphere settles slower and slower until a certain point at which the sphere suddenly accelerates and this pattern is repeated continually.
ABSTRACT We confirm numerically that the Johnson-Segalman model is able to reproduce the continua... more ABSTRACT We confirm numerically that the Johnson-Segalman model is able to reproduce the continual oscillations of the falling sphere observed in some viscoelastic models. The empirical choice of parameters used in the Johnson-Segalman model is from the ones that show the non-monotone stress-strain relation of the steady shear flows of the model. The carefully chosen parameters yield continual, self-sustaining, (ir)regular and periodic oscillations of the speed for the falling sphere through the Johnson-Segalman fluids. In particular, our simulations reproduce the phenomena: the falling sphere settles slower and slower until a certain point at which the sphere suddenly accelerates and this pattern is repeated continually.
Lecture Notes in Computational Science and Engineering, 2014
Handbook of Numerical Analysis, 2011
SPE Reservoir Characterisation and Simulation Conference and Exhibition, 2015
Parallel reservoir simulators are now widely used with availability of super computers. Modern ma... more Parallel reservoir simulators are now widely used with availability of super computers. Modern massively parallel supercomputers demonstrate great power for simulating large-scale reservoir models. However, improving scalability and efficiency for fully implicit methods on emerging parallel architectures is still challenging. In this paper, we present a robust discretization together with a parallel linear solver algorithm; and we explore the parallel implementation on the world's fastest supercomputer Tianhe-2.
Petroleum Science, 2014
As a result of the interplay between advances in computer hardware, software, and algorithm, fine... more As a result of the interplay between advances in computer hardware, software, and algorithm, fine reservoir characterization, efficient nonlinear/linear solvers, and parallel implementation. In this paper, we discuss a multilevel preconditioner in a new-generation simulator and its implementation on multicore computers. This preconditioner relies on the method of subspace corrections to solve large-scale linear systems arising from fully implicit methods in reservoir simulations. We investigate the parallel computing resources (such as high-performance clusters), desktop computers and workstations still dominate the work environment for reservoir simulation engineers. Because of the interplay of the three "walls" -the memory wall, the instruction level parallelism wall, and the power wall (the chip's overall temperature and power consumption)the peak performance of a single core has almost stopped improving. Even worse, single-core performance has started to deteriorate in some cases. There is a trend toward using multicore processors, which helps CPU designers to avoid the high power-consumption problem that comes with increasing chip frequency. As CPU speeds rise into the 3-4 GHz range, the amount of electrical power required is prohibitive. Hence, the trend toward multicore processors started and will continue into the foreseeable future. OpenMP is an application program interface that can be used to explicitly direct multicore (shared memory) parallelism. It is a and environment variables that can be used to specify shared memory parallelism in Fortran and C/C++ programs.
As we stride toward the exascale era, due to increasing complexity of supercomputers, hard and so... more As we stride toward the exascale era, due to increasing complexity of supercomputers, hard and soft errors are causing more and more problems in high-performance scientific and engineering computation. In order to improve reliability (increase the mean time to failure) of computing systems, a lot of efforts have been devoted to developing techniques to forecast, prevent, and recover from errors at different levels, including architecture, application, and algorithm. In this paper, we focus on algorithmic error resilient iterative linear solvers and introduce a redundant subspace correction method. Using a general framework of redundant subspace corrections, we construct iterative methods, which have the following properties: (1) Maintain convergence when error occurs assuming it is detectable; (2) Introduce low computational overhead when no error occurs; (3) Require only small amount of local (point-to-point) communication compared to traditional methods and maintain good load balance; (4) Improve the mean time to failure. With the proposed method, we can improve reliability of many scientific and engineering applications. Preliminary numerical experiments demonstrate the efficiency and effectiveness of the new subspace correction method. extreme-scale computer hardware and software during the last few decades (Keyes 2011). Largescale HPC installations are interrupted by data corruptions and hardware failures with increasing frequency and it becomes more and more difficult to maintain a reliable computing environment. It has been reported that the ASCI Q computer (12,288 EV-68 processors) in the Los Alamos National Laboratory experienced 26.1 radiation-induced CPU failures per week ) and a BlueGene/L (128K processors) experiences one soft error in its L1 cache every 4-6 hours due to radioactive decay in lead solder .
In this paper, we discuss an adaptive hybrid stress finite element method on quadrilateral meshes... more In this paper, we discuss an adaptive hybrid stress finite element method on quadrilateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid stress quadrilateral elements with 5 to 7 nodes. In particular, we derive a priori error estimation for the 5-node transition hybrid stress element to show that it is free from Poisson-locking, in the sense that the error bound in the a priori estimate is independent of the Lame constant $\lambda$. We introduce, for quadrilateral meshes, refinement/coarsening algorithms, which do not require storing the refinement tree explicitly, and give an adaptive algorithm. Finally we provide some numerical results.
International Journal of Numerical Analysis and Modeling
Efficient methods for solving linear algebraic equations are crucial to creating fast and accurat... more Efficient methods for solving linear algebraic equations are crucial to creating fast and accurate numerical simulations in many applications. In this paper, an algebraic multigrid (AMG) method, which combines the classical coarsening scheme by [J. W. Ruge and K. Stüben, “Algebraic multigrid”, Multigrid methods 3, 73–130 (1987)] with an energy-minimizing interpolation algorithm by [J. Xu and L. Zikatanov, Comput. Vis. Sci. 7, No. 3-4, 121–127 (2004; Zbl 1077.65130)], is employed and tested for subsurface water simulations. Based on numerical tests using real field data, our results suggest that the energy-minimizing algebraic multigrid method is efficient and, more importantly, very robust.
SPE Reservoir Characterization and Simulation Conference and Exhibition, 2013
Lecture Notes in Computational Science and Engineering, 2010
Numerische Mathematik, 2010
Abstract We consider elliptic and parabolic variational equations and inequalities governed by in... more Abstract We consider elliptic and parabolic variational equations and inequalities governed by integro-differential operators of order 2s ∈ (0, 2. Our main motivation is the pricing of European or American options under Lévy processes, in particular pure jump processes ...
Mathematical Models and Methods in Applied Sciences, 2011
Journal of Scientific Computing, 2014
In this paper, we consider the adaptive Eulerian-Lagrangian method (ELM) for linear convection-di... more In this paper, we consider the adaptive Eulerian-Lagrangian method (ELM) for linear convection-diffusion problems. Unlike the classical a posteriori error estimations, we estimate the temporal error along the characteristics and derive a new a posteriori error bound for ELM semi-discretization. With the help of this proposed error bound, we are able to show the optimal convergence rate of ELM for solutions with minimal regularity. Furthermore, by combining this error bound with a standard residual-type estimator for the spatial error, we obtain a posteriori error estimators for a fully discrete scheme.
Journal of Computational Mathematics, 2011
Journal of Computational Mathematics, 2010
In this paper, an ecient and easy-to-implement coarsening algorithm is proposed for adaptive grid... more In this paper, an ecient and easy-to-implement coarsening algorithm is proposed for adaptive grids obtained using the newest vertex bisection method in R2. The coarsening algorithm does not require storing the binary renement tree explicitly. Instead, the struc- ture is implicitly contained in the special ordering of triangular elements. This not only reduces the memory usage and CPU time, but
ABSTRACT In this paper, we revisit an auxiliary space preconditioning method proposed by Xu [Comp... more ABSTRACT In this paper, we revisit an auxiliary space preconditioning method proposed by Xu [Computing 56, 1996], in which low-order finite element spaces are employed as auxiliary spaces for solving linear algebraic systems arising from high-order finite element discretizations. We provide a new convergence rate estimate and parallel implementation of the proposed algorithm. We show that this method is user-friendly and can play an important role in a variety of Poisson-based solvers for more challenging problems such as the Navier--Stokes equation. We investigate the performance of the proposed algorithm using the Poisson equation and the Stokes equation on 3D unstructured grids. Numerical results demonstrate the advantages of the proposed algorithm in terms of efficiency, robustness, and parallel scalability.
Uploads
Papers by Chen-Song Zhang