immersed interface finite element methods for elliptic interface problems with nonhomogeneous jump conditions in this work a class of new finite element methods called immersed interface finite element methods is developed to solve elliptic interface problems with nonhomogeneous jump conditions simple non body fitted meshes are used a single function that satisfies the same nonhomogeneous jump conditions is constructed using a level set representation of the interface with such a function the discontinuities across the interface in the solution and flux are removed and an equivalent elliptic interface problem with homogeneous jump conditions is formulated special finite element basis functions are constructed for nodal points near the interface to satisfy the homogeneous jump conditions error analysis and numerical tests are presented to demonstrate that such methods have an optimal convergence rate these methods are designed as an efficient component of the finite element level set methodology for fast simulation of interface dynamics that does not require remeshing

fast finite difference approximation for identifying parameters in a two dimensional space fractional nonlocal model with variable diffusivity coefficients in this paper we consider an inverse problem for identifying the fractional derivative indices in a two dimensional space fractional nonlocal model based on a generalization of the two sided riemann liouville formulation with variable diffusivity coefficients first we derive an implicit difference method idm for the direct problem and the stability and convergence of the idm are discussed second for the implementation of the idm we develop a fast bi conjugate gradient stabilized method fbi cgstab that is superior in computational performance to gaussian elimination and attains the same accuracy third we utilize the levenberg marquardt l m regularization technique combined with the armijo rule the popular inexact line search condition to solve the modified nonlinear least squares model associated with the parameter identification finally we carry out numerical tests to verify the accuracy and efficiency of the idm numerical investigations are performed with both accurate data and noisy

on some techniques for approximating boundary conditions in the finite element method we discuss the stabilization of finite element methods in which essential boundary conditions are approximated by babuska s method of lagrange multipliers and we show that there is a close connection with this technique and a classical method by nitsche

the high order compact numerical algorithms for the two dimensional fractional sub diffusion equation in this paper performing the average operators on the space variables a numerical scheme with third order temporal convergence for the two dimensional fractional sub diffusion equation is considered for which the unconditional stability and convergence in l1 l norm are strictly analyzed for 0 0 9569347 by using the discrete energy method therewith adding small perturbation terms we construct a compact alternating direction implicit difference scheme for the two dimensional case finally some numerical results have been given to show the computational efficiency and numerical accuracy of both schemes for all 0 1

cumulative dominance and heuristic performance in binary multiattribute choice we study the effectiveness of simple heuristics in multiattribute decision making we consider the case of an additive separable utility function with nonnegative nonincreasing attribute weights in this case cumulative dominance ensures that the so called cumulative dominance compliant heuristics will choose a best alternative for the case of binary attribute values and under two probabilistic models of the decision environment generalizing a simple bernoulli model we obtain the probabilities of simple and cumulative dominance in contrast with the probability of simple dominance the probability of cumulative dominance is shown to be large in many cases explaining the effectiveness of cumulative dominance compliant heuristics in those cases additionally for the subclass of the so called fully cumulative dominance compliant heuristics we obtain an upper bound for the expected loss that only depends on the weights being nonnegative and nonincreasing the low values of the upper bound for cases in

the effect of attribute ranges on weights in multiattribute utility measurements multiattribute utility theory requires a specific relation between the range of outcomes of each attribute and the weight for that attribute the greater the range the greater the weight has to be experimental results show that subjects do not adjust their judgments properly if the range is varied for the two methods tested the adjustment is smaller than required by theory the bias was smaller for a regression procedure than for the direct ratio method weights based on an intuitive range were not found to be superior to those elicited over different ranges

attribute conflict and preference uncertainty the randmau model this paper extends the behavioral results reported in fischer et al 2000 by developing a model addressing preference uncertainty in multiattribute evaluation the model is motivated by two hypotheses regarding properties of multiattribute profiles that lead to greater preference uncertainty our attribute conflict hypothesis predicts that greater within alternative conflict discrepancy among the attributes of an alternative leads to more preference uncertainty our attribute extremity hypothesis predicts that greater attribute extremity very high or low attribute values leads to less preference uncertainty to provide a deeper explanation of attribute conflict and extremity effects we develop randmau a family of additive randauf and multiplicative randmuf random weights multiattribute utility models in randmau models preference uncertainty is represented as random variation in both the weighting parameters governing trade offs among attributes and the curvature parameters governing single attribute evaluations simulation results show that randmuf successfully predicts both the attribute conflict and attribute extremity effects exhibited by the experimental participants in fischer et al 2000 it also predicts an outcome value effect on error whose form depends on the shape of single attribute functions and on the type of multiattribute combination rule

fast inversion of triangular toeplitz matrices an algorithm requiring 0 n log n operations is proposed for the inversion of triangular toeplitz matrices this algorithm is faster than existing techniques even for relatively small values of n and can easily be written in fortran

numerical simulations of 2d fractional subdiffusion problems the growing number of applications of fractional derivatives in various fields of science and engineering indicates that there is a significant demand for better mathematical algorithms for models with real objects and processes currently most algorithms are designed for 1d problems due to the memory effect in fractional derivatives in this work the 2d fractional subdiffusion problems are solved by an algorithm that couples an adaptive time stepping and adaptive spatial basis selection approach the proposed algorithm is also used to simulate a subdiffusion convection equation

convergence of the compact finite difference method for second order elliptic equations abstract in this paper we give a fourth order compact finite difference scheme for the general forms of two point boundary value problems and two dimensional elliptic partial differential equations pde s by decomposing the coefficient matrix into a sum of several matrixes after we discretize the original problems we can obtain a lower bound for the smallest eigenvalue of the coefficient matrix thus we prove the compact finite difference scheme converges with the fourth order of accuracy to solve the discretized block tri diagonal matrix equations of the two dimensional elliptic pde s we develop an efficient iterative method full multigrid method in our numerical experiments we compare the compact finite difference method with the finite element method and crank nicolson finite difference method the results show that the compact finite difference scheme is a highly efficient and accurate method

multi attribute decision making a simulation comparison of select methods abstract several methods have been proposed for solving multi attribute decision making problems madm a major criticism of madm is that different techniques may yield different results when applied to the same problem the problem considered in this study consists of a decision matrix input of n criteria weights and ratings of l alternatives on each criterion the comparative performance of some methods has been investigated in a few mostly field studies in this simulation experiment we investigate the performance of eight methods electre topsis multiplicative exponential weighting mew simple additive weighting saw and four versions of ahp original vs geometric scale and right eigenvector vs mean transformation solution simulation parameters are the number of alternatives criteria and their distribution the solutions are analyzed using twelve measures of similarity of performance similarities and differences in the behavior of these methods are investigated dissimilarities in weights produced by these methods become stronger in problems with few alternatives however the corresponding final rankings of the alternatives vary across methods more in problems with many alternatives although less significant the distribution of criterion weights affects the methods differently in general all ahp versions behave similarly and closer to saw than the other methods electre is the least similar to saw except for closer matching the top ranked alternative followed by mew topsis behaves closer to ahp and differently from electre and mew except for problems with few criteria a similar rank reversal experiment produced the following performance order of methods saw and mew best followed by topsis ahps and electre it should be noted that the electre version used was adapted to the common madm problem and therefore it did not take advantage of the method s capabilities in handling problems with ordinal or imprecise information

further developments and tests of a progressive algorithm for multiple criteria decision making p korhonen h moskowitz and j wallenius 1986 developed a progressive algorithm and the supporting theory for modeling and solving multiple criteria decision problems with discrete alternatives a special feature of the algorithm is that it relaxes the usual assumption of a fixed set of available decision alternatives and complete knowledge of a decision maker s dm s preference structure or value function the algorithm is based on progressively sampling the decision space obtaining preference information from the dm determining the likelihood of finding possibly surely better alternatives and based on this information continuing the search or terminating it by making the final choice we describe a computerized implementation and extensive computational tests of the algorithm as well as some of our experiences in applying and field testing it in practice we also consider several improvements and developments of the algorithm to further facilitate its use in practice

on the sobolev space of isometric immersions we prove that every w 2 2 isometric immersion from a convex regular domain of r 2 into r3 can be approximated in w 2 2 norm by smooth isometric immersions from the same domain into r3

aggregation of utility based individual preferences for group decision making abstract multi attribute utility theory maut elicits an individual decision maker s preferences for single attributes and develops a utility function by mathematics formulation to add up the preferences of the entire set of attributes when assessing alternatives a common aggregation method of maut for group decisions is the simple additive weighting saw method which does not consider the different preferential levels and preferential ranks for individual decision makers assessments of alternatives in a decision group and thus seems too intuitive in achieving the consensus and commitment for group decision aggregation in this paper the preferential differences denoting the preference degrees among different alternatives and preferential priorities denoting the favorite ranking of the alternatives for each decision maker are both considered and aggregated to construct the utility discriminative values for assessing alternatives in a decision group a comparative analysis is performed to compare the proposed approach to the saw model and a satisfaction index is used to investigate the satisfaction levels of the final two resulting group decisions in addition a feedback interview is conducted to understand the subjective perceptions of decision makers while examining the results obtained from these two approaches for the second practical case both investigation results show that the proposed approach is able to achieve a more satisfying and agreeable group decision than that of the saw method

group decision making using bilateral agreement matrix abstract group decision making based on a bilateral agreement matrix is investigated in this paper to derive a group decision from the opinions of individual decision makers pairs of decision makers are allowed to negotiate with one another and provide their bilateral negotiation values two algorithms are provided to help pairs of decision makers reach bilateral agreements which enables the construction of the bilateral agreement matrix the definition of a consistent bilateral agreement matrix is introduced to measure the credibility of the final result and its properties are investigated based on which a method is provided to construct a consistent bilateral agreement matrix from an inconsistent one models are then given to derive the weight vector from the bilateral agreement matrix based on which a consistency index of the matrix is defined two algorithms are then given to improve the level of consistency of the bilateral agreement matrix the final group decision is obtained by aggregating individual opinions using the weight vector the proposed methods are further extended to deal with the problem of incomplete bilateral agreement matrices several examples are also given to illustrate the proposed approach

using hierarchical matrices in the solution of the time fractional heat equation by multigrid waveform relaxation abstract this work deals with the efficient numerical solution of the time fractional heat equation discretized on non uniform temporal meshes non uniform grids are essential to capture the singularities of typical solutions of time fractional problems we propose an efficient space time multigrid method based on the waveform relaxation technique which accounts for the nonlocal character of the fractional differential operator to maintain an optimal complexity which can be obtained for the case of uniform grids we approximate the coefficient matrix corresponding to the temporal discretization by its hierarchical matrix h matrix representation in particular the proposed method has a computational cost of o k n m log m where m is the number of time steps n is the number of spatial grid points and k is a parameter which controls the accuracy of the h matrix approximation the efficiency and the good convergence of the algorithm which can be theoretically justified by a semi algebraic mode analysis are demonstrated through numerical experiments in both one and two dimensional spaces

multi criteria group decision making based on bilateral agreements abstract in multi criteria group decision making a key issue is aggregating individual preference into group one in this study we employ a bilateral agreement to conduct group evaluation of alternatives the bilateral agreement between a pair of individuals could be on the weight of a criterion a criterion evaluation function or willingness to pay any one of three types of bilateral agreements can derive the group utility to express the relationship between the bilateral agreement and individual evaluations the quasi arithmetic mean is used which can ensure the consistency property of the pairwise comparison matrices the minimum requirements are explored to obtain the group preference which shows that n 1 pairs of bilateral agreements are necessary finally several examples are provided to illustrate the proposed methods

numerical algorithms for time fractional subdiffusion equation with second order accuracy this article aims to fill in the gap of the second order accurate schemes for the time fractional subdiffusion equation with unconditional stability two fully discrete schemes are first proposed f

fast inversion of triangular toeplitz matrices in this paper we present an approximate inversion method for triangular toeplitz matrices based on trigonometric polynomial interpolation to obtain an approximate inverse of high accuracy for a triangular toeplitz matrix of size n our algorithm requires two fast fourier transforms ffts and one fast cosine transform of 2n vectors we then revise the approximate method proposed by bini siam j comput 13 1984 268 the complexity of the revised bini algorithm is two ffts of 2n vectors

parallel solution of certain toeplitz linear systems using the concept of approximate algorithm it is shown that 6 log n 6 parallel steps and 2n processors suffice to approximate with any precision the solution of a linear system with an n times n triangular toeplitz matrix a moreover 7 log n 7 steps are sufficient for an exact computation whereas the number of processors is increased to frac 5 2 n 2 if a is also banded and k is its bandwidth the number of processors is reduced to frac 5 2 n k 1 two applications are shown it is proved that if b is any matrix belonging to the algebra generated over the complex field by a given n times n matrix then the system bx b can be solved with no more than 9 log n 4 steps with o n 2 processors it is proved that given a toeplitz matrix a a i j such that a i j 0 if i j k or j i h a k 1 ne 0 then 13 log n o log 2 k steps and max frac 5 2 n k h n n 1 2 processors are sufficient to solve the system ax

the kirchhoff theory for elastic pre strained shells abstract applying methods of convergence we introduce and justify a variant of the kirchhoff theory for pre strained shells the effective 2d energy represents bending relative to the desired riemannian metric we also develop the analogue of this theory in the presence of the incompressibility constraint with respect to the metric

a fast accurate approximation method with multigrid solver for two dimensional fractional sub diffusion equation a fast accurate approximation method with multigrid solver is proposed to solve a two dimensional fractional sub diffusion equation using the finite difference discretization of fractional time derivative a block lower triangular toeplitz matrix is obtained where each main diagonal block contains a two dimensional matrix for the laplacian operator our idea is to make use of the block circulant approximation via fast fourier transforms so that the resulting task is to solve a block diagonal system where each diagonal block matrix is the sum of a complex scalar times the identity matrix and a laplacian matrix we show that the accuracy of the approximation scheme is of o because of the special diagonal block structure we employ the multigrid method to solve the resulting linear systems the convergence of the multigrid method is studied numerical examples are presented to illustrate the accuracy of the proposed approximation scheme and the efficiency of the proposed solver an approximation method is proposed to approximate the original block lower triangular toeplitz linear system sufficient condition is given to guarantee a high accuracy of the approximation method multigrid solver is employed to solve the resulting block diagonal linear system multigrid solver is proven to be linear convergence numerical examples illustrate the accuracy of the proposed approximation scheme and the efficiency of the proposed solver

a new difference scheme for the time fractional diffusion equation abstract in this paper we construct a new difference analog of the caputo fractional derivative called the l 2 1 formula the basic properties of this difference operator are investigated and on its basis some difference schemes generating approximations of the second and fourth order in space and the second order in time for the time fractional diffusion equation with variable coefficients are considered stability of the suggested schemes and also their convergence in the grid l 2 norm with the rate equal to the order of the approximation error are proved the obtained results are supported by the numerical calculations carried out for some test problems

the use of finite difference element approaches for solving the time fractional subdiffusion equation in this paper two finite difference element approaches for the time fractional subdiffusion equation with dirichlet boundary conditions are developed in which the time direction is approximated by the fractional linear multistep method and the space direction is approximated by the finite element method the two methods are unconditionally stable and convergent of order o tau q h r 1 in the l 2 norm where q 2 beta or 2 when the analytical solution to the subdiffusion equation is sufficiently smooth beta 0 beta 1 is the order of the fractional derivative tau and h are the step sizes in time and space respectively and r is the degree of the polynomial space the corresponding schemes for the subdiffusion equation with neumann boundary conditions are presented as well where the stability and convergence are shown numerical examples are provided to verify the theoretical analysis comparisons between the algorithms derived in this paper and the existing algorithms are given

group decisions with multiple criteria we consider a decision problem where a group of individuals evaluates multiattribute alternatives we explore the minimal required agreements that are sufficient to specify the group utility function a surprising result is that under some conditions a bilateral agreement among pairs of individuals on a single attribute is sufficient to derive the multiattribute group utility the bilateral agreement between a pair of individuals could be on the weight of an attribute on an attribute evaluation function or on willingness to pay we focus on the case in which each individual s utility function is additive we show that the group utility can be represented as the weighted sum of group attribute weights and more remarkably of attribute evaluation functions these group attribute evaluation functions are in turn weighted sums of individual attribute evaluation functions

multiple criteria decision making multiattribute utility theory the next ten years management science and decision science have grown exponentially since midcentury two closely related fields central to this growth are multiple criteria decision making mcdm and multiattribute utility theory maut this paper comments on the history of mcdm and maut and discusses topics we believe are important in their continued development and usefulness to management science over the next decade our aim is to identify exciting directions and promising areas for future research