an immersed boundary method with formal second order accuracy and reduced numerical viscosity a formally second order accurate immersed boundary method is presented and tested in this paper we apply this new scheme to simulate the flow past a circular cylinder and study the effect of numerical viscosity on the accuracy of the computation by comparing the numerical results with those of a first order method the numerical evidence shows that the new scheme has less numerical viscosity and is therefore a better choice for the simulation of high reynolds number flows with immersed boundaries

optimal multiple objective resource allocation using hybrid particle swarm optimization and adaptive resource bounds technique the multiple objective resource allocation problem morap seeks for an allocation of resource to a number of activities such that a set of objectives are optimized simultaneously and the resource constraints are satisfied morap has many applications such as resource distribution project budgeting software testing health care resource allocation etc this paper addresses the nonlinear morap with integer decision variable constraint to guarantee that all the resource constraints are satisfied we devise an adaptive resource bound technique to construct feasible solutions the proposed method employs the particle swarm optimization pso paradigm and presents a hybrid execution plan which embeds a hill climbing heuristic into the pso for expediting the convergence to cope with the optimization problem with multiple objectives we evaluate the candidate solutions based on dominance relationship and a score function experimental results manifest that the hybrid pso derives solution sets which are very close to the exact pareto sets the proposed method also outperforms several representatives of the state of the art algorithms on a simulation data set of the morap

pseudospectral least squares method for stokes darcy equations we investigate the first order system least squares legendre and chebyshev pseudospectral method for coupled stokes darcy equations a least squares functional is defined by summing up the weighted l 2 norm of residuals of the first order system for coupled stokes darcy equations and that of beavers joseph saffman interface conditions continuous and discrete homogeneous functionals are shown to be equivalent to a combination of weighted h div and h 1 norms for stokes and darcy equations the spectral convergence for the legendre and chebyshev methods is derived some numerical experiments are demonstrated to validate our analysis

immersed interface methods for stokes flow with elastic boundaries or surface tension a second order accurate interface tracking method for the solution of incompressible stokes flow problems with moving interfaces on a uniform cartesian grid is presented the interface may consist of an elastic boundary immersed in the fluid or an interface between two different fluids the interface is represented by a cubic spline along which the singularly supported elastic or surface tension force can be computed the stokes equations are then discretized using the second order accurate finite difference methods for elliptic equations with singular sources developed in our previous paper siam j numer anal 31 1994 pp 1019 1044 the resulting velocities are interpolated to the interface to determine the motion of the interface an implicit quasi newton method is developed that allows reasonable time steps to be used

on the convergence of finite element solutions to the interface problem for the stokes system the stokes system with a discontinuous coefficient stokes interface problem and its finite element approximations are considered we firstly show a general error estimate to derive explicit convergence rates we introduce some appropriate assumptions on the regularity of exact solutions and on a geometric condition for the triangulation we mainly deal with the mini element approximation and then consider p1 iso p2 p1 element approximation results are expected to give an instructive remark in numerical analysis for two phase flow problems

first order system least squares for coupled stokes darcy flow the coupled problem with stokes flow in one subdomain and a darcy flow model in a second subdomain is studied in this paper both flow problems are treated as first order systems involving pseudostress and velocity in the stokes case and using a flux pressure formulation in the darcy subdomain as process variables respectively the beavers joseph saffman interface conditions are treated by an appropriate interface functional which is added to the least squares functional associated with the subdomain problems a combination of h mathrm div conforming raviart thomas and standard h 1 conforming elements is used for the stokes as well as for the darcy subsystem the homogeneous least squares functional is shown to be equivalent to an appropriate norm allowing the use of standard finite element approximation estimates it also establishes the fact that the local evaluation of the least squares functional itself constitutes an a posteriori error estimator to be used for adaptive refinement strategies

an effective modified binary particle swarm optimization mbpso algorithm for multi objective resource allocation problem morap a modified binary particle swarm optimization mbpso algorithm is proposed for solving the multi objective resource allocation problem morap first the generation mechanism for initial particles is established to guarantee that the algorithm can begin to search optimal particle in the feasible solution space second we develop the update mechanism for iterative particles which includes setting up the memory array modifying sig function and verifying the constraint condition to assure that the regenerated particles meet the constraint and algorithm can quickly converge third the selection mechanism for pbesti and gbest is proposed which uses the dynamic neighborhood strategy to ensure that the algorithm to find pareto optimal solutions through comparing the example simulation results of our mbpso with hga and aco published in references we find that proposed mbpso outperforms hga and aco finally the effectiveness of the different improved methods is analyzed and the synergism effect and the convergence behavior of the mbpso algorithm show its good performances

a family of higher order mixed finite element methods for plane elasticity the dirichler problem for the equations of plane elasticity is approximated by a mixed finite element method using a new family of composite finite elements having properties analogous to those possessed by the raviart thomas mixed finite elements for a scalar second order elliptic equation estimates of optimal order and minimal regularity are derived for the errors in the displacement vector and the stress tensor inl 2 and optimal order negative norm estimates are obtained inh s for a range ofs depending on the index of the finite element space an optimal order estimate inl for the displacement error is given also a quasioptimal estimate is derived in an appropriate space all estimates are valid uniformly with respect to the compressibility and apply in the incompressible case the formulation of the elements is presented in detail

fast convolutions meet montgomery arithmetic in large ring and field extensions is an important problem of symbolic computation and it consists essentially of the combination of one multiplication and one division in the underlying ring methods are known for replacing one division by two short multiplications in the underlying ring which can be performed essentially by using convolutions however while using school book multiplication modular multiplication may be grouped into 2m r operations where m r denotes the number of operations of one multiplication in the underlying ring the short multiplication problem is an important obstruction to convolution it raises the costs in that case to 3m r in this paper we give a method for understanding and bypassing this problem thus reducing the costs of ring arithmetic to roughly 2m r when also using fast convolutions the algorithms have been implemented with results which fit well the theoretical prediction and which shall be presented in a separate paper

new frameworks for montgomery s modular multiplication method we present frameworks for fast modular multiplication based on a modification of montgomery s original method for fixed large integers our algorithms may be significantly faster than conventional methods our techniques may also be extended to modular polynomial arithmetic

first order system least squares method for the interface problem of the stokes equations the first order system least squares method for the stokes equation with discontinuous viscosity and singular force along the interface is proposed and analyzed first interface conditions are derived by introducing a physical meaningful variable such as the velocity gradient the stokes equation transformed into a first order system of equations then the continuous and discrete norm least squares functionals using legendre and chebyshev weights for the first order system are defined we showed that continuous and discrete homogeneous least squares functionals are equivalent to appropriate product norms the spectral convergence of the proposed method is given a numerical example is provided to support the method and its analysis

the immersed interface method for elliptic equations with discontinuous coefficients and singular sources the authors develop finite difference methods for elliptic equations of the form nabla cdot beta x nabla u x kappa x u x f x in a region omega in one or two space dimension

numerical simulation of two dimensional flows over a circular cylinder using the immersed boundary method in this work a virtual boundary method is applied to the numerical simulation of a uniform flow over a cylinder the force source term added to the two dimensional navier stokes equations guarantees the imposition of the no slip boundary condition over the body fluid interface these equations are discretized using the finite differences method the immersed boundary is represented with a finite number of lagrangian points distributed over the solid fluid interface a cartesian grid is used to solve the fluid flow equations the key idea is to propose a method to calculate the interfacial force without ad hoc constants that should usually be adjusted for the type of flow and the type of the numerical method when this kind of model is used in the present work this force is calculated using the navier stokes equations applied to the lagrangian points and then distributed over the eulerian grid the main advantage of this approach is that it enables calculation of this force field even if the interface is moving or deforming it is unnecessary to locate the eulerian grid points near this immersed boundary the lift and drag coefficients and the strouhal number calculated for an immersed cylinder are compared with previous experimental and numerical results for different reynolds numbers

implementing the asymptotically fast version of the elliptic curve primality proving algorithm the elliptic curve primality proving ecpp algorithm is one of the current fastest practical algorithms for proving the primality of large numbers its running time cannot be proven rigorously but heuristic arguments show that it should run in time o log n 5 to prove the primality of n an asymptotically fast version of it attributed to j o shallit runs in time o log n 4 the aim of this article is to describe this version in more details leading to actual implementations able to handle numbers with several thousands of decimal digits

an effective genetic algorithm approach to multiobjective resource allocation problems moraps dynamic programming dp is a mathematical procedure designed primarily to improve the computational efficiency of solving select mathematical programming problems by decomposing them into smaller and hence computationally simpler subproblems in solving multiple objectives dynamic programming problem modp classical approaches reduce the multiple objectives into a single objective of minimizing a weighted sum of objectives the determination of these weights indicate the relative importance of the various objective also if the problem scale increases it become difficult to be dealt with even in the case of single objective because of the rapid expansion of the number of states to be considered in this paper we investigated the possibility of using genetic algorithms gas to solve multiobjective resource allocation problems moraps this procedure eliminates the need of any user defined weight factor for each objective also the proposed approach is developed to deal with the problems with both single or multiple objectives the simulation results for multiobjective resource allocation problems morap shows that genetic algorithms gas may hopefully be a new approach for such kinds of problems

a hybrid binary particle swarm optimization for the obnoxious p median problem abstract the obnoxious p median problem can be formulated as a constrained binary linear program it is np hard and has a lot of real world applications in this paper a hybrid binary particle swarm optimization is proposed to solve the obnoxious p median problem a new position updating rule is presented to inherit the good structure of previous high quality solutions furthermore two tabu based mutation operators are used to avoid the premature convergence and guide the search to a promising area a greedy repair procedure is developed to repair infeasible solutions in addition an iterated greedy local search procedure is utilized to enhance the exploitation ability extensive experiments are done on a set of 72 benchmark instances from the literature experimental results and comparisons with some existing algorithms demonstrate the effectiveness of the proposed algorithm in particular the proposed algorithm finds new best solutions for 15 instances compared with existing algorithms the proposed algorithm is able to find better average objective function value in a short average computing time

the least squares pseudo spectral method for navier stokes equations a spectral collocation approximation of first order system least squares for incompressible stokes equations was analyzed in kim et al 2004 12 and finite element approximations for incompressible navier stokes equations were developed in bochev et al 1998 1999 9 10 the aim of this paper is to analyze the first order system least squares pseudo spectral method for incompressible navier stokes equations the paper will be an extension of the result in kim et al 2004 12 to the navier stokes equations our least squares functional is defined by the sum of discrete spectral norms of a first order system of equations corresponding to the navier stokes equations based on legendre gauss lobatto points we show its ellipticity and continuity over an appropriate product space and spectral convergences of discretization errors are derived in the h 1 norm and the l 2 norm in each variable finally we present some numerical examples

modular multiplication without trial division let n 1 we present a method for multiplying two integers called n residues modulo n while avoiding division by n n residues are represented in a nonstandard way so this method is useful only if several computations are done modulo one n the addition and subtraction algorithms are unchanged 1 description some algorithms 1 2 4 5 require extensive modular arith metic we propose a representation of residue classes so as to speed modular multiplication without affecting the modular addition and subtraction algorithms other recent algorithms for modular arithmetic appear in 3 6 fix n 1 define an a residue to be a residue class modulo n select a radix r coprime to n possibly the machine word size or a power thereof such that r n and such that computations modulo r are inexpensive to process let r l and n be integers satisfying 0 n then return t n else return t to validate redc observe mn tn n tmod r so t is an integer also tr tmod n so t tr x mod n thirdly 0 t mn rn rn so 0 t 2n if r and n are large then t mn may exceed the largest double precision value one can circumvent this by adjusting m so r m 0 given two numbers x and y between 0 and n 1 inclusive let z redc xy then z xy r x mod n so xr l yr x zrx mod n also 0 z n so z is the product of x and y in this representation other algorithms for operating on n residues in this representation can be derived from the algorithms normally used the addition algorithm is unchanged since xr x yr x zr x mod n if and only if x y z mod n also unchanged are

least squares spectral method for the two dimensional stokes interface problems abstract this paper deals with the pseudo spectral least squares method to approximate the solution of the stokes interface problem that is the stokes equations with discontinuous viscosity and singular source term the stokes interface equations are adjusted in each sub domain along with the interface conditions then the equations are reformulated as a first order system by introducing stress tensor as a new independent variable the continuous and discrete norm least squares functionals using legendre and chebyshev weights for the first order system are defined and shown to be equivalent to appropriate product norms the spectral convergence of the proposed method is presented numerical examples are also given to demonstrate the method and analysis