
Nguyen, Vinh Tan; Khoo, Boo Cheong; Peraire, Jaime; Persson, PerOlof
Shock capturing has been a challenge for computational fluid dynamicists over the years. This article deals with discontinuous Galerkin method to solve the hyperbolic equations in which solutions may develop discontinuities in finite time. The high order discontinuous Galerkin method combining the basis of finite volume and finite element methods has shown a lot of attractive features for a wide range of applications. Various techniques proposed in the literature to deal with discontinuities basically reduce the order of interpolation in the region around these discontinuities. The accuracy of the scheme therefore may be degraded in the vicinity of the shock....

Huynh, Dinh Bao Phuong; Peraire, Jaime; Patera, Anthony T.; Liu, Guirong
Modern engineering analysis requires accurate, reliable and efficient evaluation of outputs of interest. These outputs are functions of "input" parameter that serve to describe a particular configuration of the system, typical input geometry, material properties, or boundary conditions and loads. In many cases, the inputoutput relationship is a functional of the field variable  which is the solution to an inputparametrized partial differential equations (PDE). The reducedbasis approximation, adopting offline/online computational procedures, allows us to compute accurate and reliable functional outputs of PDEs with rigorous error estimations. The operation count for the online stage depends only on a small number...

Nguyen, Ngoc Son; Lim, KianMeng; White, Jacob K.
We present the application of the boundary integral equation method for solving the motion of biological cell or particle under Stokes flow in the presence of electrostatic field. The huge dense matrixvector product from the boundary integral method poses a computationally challenging problem for solving the large system of equations generated. In our work, we used the precorrectedFFT (pFFT) method to reduce the computational time and memory usage drastically, so that large scale simulations can be performed quickly on a personal computer. Results on the force field acting on the particle, as well as the behavior of the particle through...

Tan, Lian Hing; Lim, Kian Meng; White, Jacob K.
Electrostatics interaction plays a very important role in almost all biomolecular systems. The PoissonBoltzmann equation is widely used to treat this electrostatic effect in an ionic solution. In this work, a simple mixed discretecontinuum model is considered and boundary element method is used to solve for the solution.

MyHa, D.; Lim, K. M.; Khoo, Boo Cheong; Willcox, Karen E.
In this paper, a new methodology for predicting fluid free surface shape using Model Order Reduction (MOR) is presented. Proper Orthogonal Decomposition combined with a linear interpolation procedure for its coefficient is applied to a problem involving bubble dynamics near to a free surface. A model is developed to accurately and efficiently capture the variation of the free surface shape with different bubble parameters. In addition, a systematic approach is developed within the MOR framework to find the best initial locations and pressures for a set of bubbles beneath the quiescent free surface such that the resultant free surface attained...

Rosales, C.; Lim, K. M.; Khoo, Boo Cheong
This work presents detailed numerical calculations of the dielectrophoretic force in octupolar traps designed for singlecell trapping. A trap with eight planar electrodes is studied for spherical and ellipsoidal particles using an indirect implementation of the boundary element method (BEM). Multipolar approximations of orders one to three are compared with the full Maxwell stress tensor (MST) calculation of the electrical force on spherical particles. Ellipsoidal particles are also studied, but in their case only the dipolar approximation is available for comparison with the MST solution. The results show that the full MST calculation is only required in the study of...

Chai, JooSiong; Toh, Kim Chuan
We study the preconditioning of symmetric indefinite linear systems of equations that arise in interior point solution of linear optimization problems. The preconditioning method that we study exploits the block structure of the augmented matrix to design a similar block structure preconditioner to improve the spectral properties of the resulting preconditioned matrix so as to improve the convergence rate of the iterative solution of the system. We also propose a twophase algorithm that takes advantage of the spectral properties of the transformed matrix to solve for the Newton directions in the interiorpoint method. Numerical experiments have been performed on some...

Willis, David; Peraire, Jaime; White, Jacob K.
In this paper a precorrected FFTFast Multipole Tree (pFFTFMT) method for solving the potential flow around arbitrary three dimensional bodies is presented. The method takes advantage of the efficiency of the pFFT and FMT algorithms to facilitate more demanding computations such as automatic wake generation and handsoff steady and unsteady aerodynamic simulations. The velocity potential on the body surfaces and in the domain is determined using a pFFT Boundary Element Method (BEM) approach based on the Green’s Theorem Boundary Integral Equation. The vorticity trailing all lifting surfaces in the domain is represented using a Fast Multipole Tree, time advected, vortex...

Le, DucVinh; Khoo, Boo Cheong; Peraire, Jaime
We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the noslip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of singular forces is determined by solving a small system of equations at each time step. The NavierStokes...

Nguyen, Vinh Tan; Khoo, Boo Cheong; Peraire, Jaime
The discontinuities in the solutions of systems of conservation laws are widely considered as one of the difficulties in numerical simulation. A numerical method is proposed for solving these partial differential equations with discontinuities in the solution. The method is able to track these sharp discontinuities or interfaces while still fully maintain the conservation property. The motion of the front is obtained by solving a Riemann problem based on the state values at its both sides which are reconstructed by using weighted essentially non oscillatory (WENO) scheme. The propagation of the front is coupled with the evaluation of "dynamic" numerical...

Nguyen, N. C.; Liu, Guirong; Patera, Anthony T.
We present a technique for the rapid and reliable
evaluation of linearfunctional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reducedbasis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to decouple the generation and projection stages of...

Nhan, PhanThien; Fan, XiJun
In this paper, the complete double layer boundary integral equation formulation for Stokes flows is extended to viscoelastic fluids to solve the mobility problem for a system of particles, where the nonlinearity is handled by particular solutions of the Stokes inhomogeneous equation. Some techniques of the meshless method are employed and a pointwise solver is used to solve the viscoelastic constitutive equation. Hence volume meshing is avoided. The method is tested against the numerical solution for a sphere settling in the OdroydB fluid and some results on a prolate motion in shear flow of the OldroydB fluid are reported and...

RewieÅski, MichaÅ
In this paper we present an approach to the nonlinear model reduction based on representing the nonlinear system with a piecewiselinear system and then reducing each of the pieces with a Krylov projection. However, rather than approximating the individual components to make a system with exponentially many different linear regions, we instead generate a small set of linearizations about the state trajectory which is the response to a 'training input'. Computational results and performance data are presented for a nonlinear circuit and a micromachined fixedfixed beam example. These examples demonstrate that the macromodels obtained with the proposed reduction algorithm are...

Shu, Jia; Teo, Chung Piaw; Shen, ZuoJun Max
In this paper, we study the stochastic transportationinventory network design problem involving one supplier and multiple retailers. Each retailer faces some uncertain demand. Due to this uncertainty, some amount of safety stock must be maintained to achieve suitable service levels. However, riskpooling benefits may be achieved by allowing some retailers to serve as distribution centers (and therefore inventory storage locations) for other retailers. The problem is to determine which retailers should serve as distribution centers and how to allocate the other retailers to the distribution centers. Shen et al. (2000) and Daskin et al. (2001) formulated this problem as a...

Hadjiconstantinou, Nicolas G.; Garcia, Alejandro L.
We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Expressions for the fluid velocity, density and temperature are derived using equilibrium statistical mechanics. The results show that the number of samples needed to adequately resolve the flowfield scales as the inverse square of the Mach number. The theoretical results are verified for a dilute gas using direct Monte Carlo simulations. The agreement between theory and simulation verifies that the use of equilibrium theory is justified.

Toh, Kim Chuan; Cai, Zhi; Freund, Robert M.
Many optimization problems can be formulated as second order cone programming (SOCP) problems. Theoretical results show that applying interiorpoint method (IPM) to SOCP has global polynomial convergence. However, various stability issues arise in the implementation of IPM. The standard normal equation based implementation of IPM encounters stability problems in the computation of search direction. In this paper, an augmented system approach is proposed to overcome the stability problems. Numerical experiments show that the new approach can improve the stability.

Xu, Sheng; Freund, Robert M.; Sun, Jie
Given a set of circles C = {c₁, ..., cn}on the Euclidean plane with centers {(a₁, b₁), ..., (an, b_{n})}and radii {r₁..., r

Cheng, Yong Leong
Automated Guided Vehicle (AGV) ContainerJob deployment is essentially a vehicledispatching problem. In this problem, the impact of vehicle dispatching polices on the ship makespan for discharging and/or loading operations is analyzed. In particular, given a storage location for each container to be discharged from the ship and given the current location of each container to be loaded onto the ship, the problem is to propose an efficient deployment scheme to dispatch vehicles to containers so as to minimize the makespan of the ship so as to increase the throughput. The makespan of the ship refers to the time a ship...

Lin, G.C.; Peraire, Jaime; Khoo, Boo Cheong; Perakis, Georgia
The calculation of path travel times is an essential component for the dynamic traffic assignment and equilibrium problems. This paper presents a simulation method for calculating actual path travel times for the traffic network with dynamic demands. The method is based on a pathbased macroscopic simulation model of network traffic dynamics. There is no need to explicitly model intersection delays in this method. Discontinuity in the travel time caused by traffic light control can be captured by this method. It's flexible in terms that the model is not limited to a specific velocitydensity relationship. Some numerical results for signalized and...

Xu, Y.G.; Liu, Guirong
A simple but effective evolutionary algorithm is proposed in this paper for solving complicated optimization problems. The new algorithm presents two hybridization operations incorporated with the conventional genetic algorithm. It takes only 4.1% ~ 4.7% number of function evaluations required by the conventional genetic algorithm to obtain global optima for the benchmark functions tested. Application example is also provided to demonstrate its effectiveness.