Augmented Lagrangian method is a well established tool for the solution of optimization problems with equality constraints. If combined with effective algorithms for the solution of bound constrained quadratic programming problems, it can solve efficiently very large problems with bound and linear equality constraints. The point of this paper is to show that the performance of the algorithm can be

The purpose of this study is to construct a new efficient iterative method of successive approximation based on the three-point Simpson quadrature rule for solving three-dimensional nonlinear Fredholm integral equations. We have also provided the convergence and error analysis of the proposed method. Furthermore, we present the numerical stability analysis of the method with respect to the choice of

We present a general strategy for developing structure and property preserving numerical algorithms for thermodynamically consistent models of incompressible multiphase polymer solutions with a variable mobility. We first present a formalism to derive thermodynamically consistent, incompressible, multiphase polymer models. Then, we develop the general strategy, known as the supplementary variable method

We are concerned with the eigenvector-dependent nonlinear eigenvalue problem (NEPv) H(V)V=VΛ, where H(V)∈ℂn×n is a Hermitian matrix-valued function of V∈ℂn×k with orthonormal columns, i.e., VHV=Ik, k≤n (usually k≪n). Sufficient conditions on the solvability and solution uniqueness of NEPv are obtained, based on the well-known results from the relative perturbation theory. These results are complementary

In this article, we propose a Krasnosel’skiǐ-Mann-type algorithm for finding a common fixed point of a countably infinite family of nonexpansive operators (Tn)n≥0 in Hilbert spaces. We formulate an asymptotic property which the family (Tn)n≥0 has to fulfill such that the sequence generated by the algorithm converges strongly to the element in ⋂n≥0FixTn with minimum norm. Based on this, we derive a

In researching the Helmholtz equation, the focus has either been on the accuracy of the numerical solution (pollution) or the acceleration of the convergence of a preconditioned Krylov-based solver (scalability). While it is widely recognized that the convergence properties can be investigated by studying the eigenvalues, information from the eigenvalues is not used in studying the numerical dispersion

Many complex phenomena can be modeled by networks, that is, by a set of nodes connected by edges. Networks are represented by graphs, and several algebraic and analytical methods have been developed for their study. However, in order to obtain a more useful representation of a system, it is often appropriate to include more information about the nodes and/or edges, and those additions make it necessary

In this paper we study a weighted time-fractional asymptotical regularization method for solving linear ill-posed problems Ax=y where only noisy data yδ with ‖yδ−y‖≤δ are available and A is a linear bounded operator. This regularization method can be considered as a preconditioned version for the newly-developed time-fractional asymptotical regularization method. Error analysis and numerical tests

By discretising space into compartments and letting system dynamics be governed by the reaction–diffusion master equation, it is possible to derive and simulate a stochastic model of reaction and diffusion on an arbitrary domain. However, there are many implementation choices involved in this process, such as the choice of discretisation and method of derivation of the diffusive jump rates, and it

This article proposes a structured diagonal Hessian approximation for solving non–linear least-squares (NLS) problems. We devised a modified structured matrix that satisfies the weak secant equation. This structured matrix is then used to derive the structured diagonal approximation of the Hessian in a similar pattern as the paper of Andrei (2019). By solving a minimization problem, we derived the

The well-known stochastic Lotka–Volterra model for interacting multi-species in ecology has some typical features: highly nonlinear, positive solution and multi-dimensional. The known numerical methods including the tamed/truncated Euler–Maruyama (EM) applied to it do not preserve its positivity. The aim of this paper is to modify the truncated EM to establish a new positive preserving truncated EM

Preserving conservative and dissipative properties of dynamical systems is desirable in numerical integration. To this end, we develop and implement numerical methods that preserve the exact rate of dissipation in certain qualitative properties of dissipatively perturbed constrained Hamiltonian systems, which are shown to be conformal symplectic. Projection methods based on exponential Runge–Kutta

We describe a method for analyzing the structure of a system of nonlinear integro-differential–algebraic equations (IDAEs) that generalizes the Σ-method for the structural analysis of differential–algebraic equations. The method is based on the sparsity pattern of the IDAE and the ν-smoothing property of a Volterra integral operator. It determines which equations and how many times they need to be

The article deals with the numerical simulation of flows with laminar to turbulent transition due to the separation of boundary layer. Mathematical model consists of the Reynolds averaged Navier–Stokes equations which are completed by the explicit algebraic Reynolds stress model (EARSM) of turbulence. The EARSM model is enhanced with algebraic model of bypass transition which is further modified by

In this paper we consider multi-dimensional Partial Differential Equations (PDE) of parabolic type in divergence form. The coefficient matrix of the divergence operator is assumed to be discontinuous along some smooth interface. At this interface, the solution of the PDE presents a compatibility transmission condition of its co-normal derivatives (multi-dimensional diffraction problem). We prove an

In Han and Wang (2020), a 2D diffeomorphic image registration model is proposed to eliminate mesh folding. To solve the 2D diffeomorphic model, a diffeomorphic fractional-order image registration algorithm(DFIRA for short) is proposed in Han and Wang (2020). DFIRA achieves a satisfactory image registration result but it costs too much CPU time. To accelerate DFIRA, we propose a fast multi grid algorithm

Power flow computations are important for operation and planning of the electricity grid, but are computationally expensive because of nonlinearities and the size of the system of equations. Linearized methods reduce computational time but often have the disadvantage that they are not applicable to general grids. In this paper we propose a novel linearized power flow (LPF) technique that is able to

In this paper, we first propose a new block splitting (NBS) iteration method for solving the large sparse complex symmetric linear systems. The NBS iteration method avoids complex arithmetic compared with the combination method of real part and imaginary part (CRI) one established by Wang et al. (2017). The unconditional convergence and the quasi-optimal parameter of the NBS iteration method are given

In this paper, based on the previous published work by Wang et al. [Modified Newton-type iteration methods for generalized absolute value equations, Wang et al. (2019), by using the matrix splitting technique, Newton-based matrix splitting iterative method is established to solve the generalized absolute value equation. The proposed method not only covers the above modified Newton-type iterative method

Radial basis functions is a simple and accurate method for multivariate interpolation but the ill–conditioning situation due to their interpolation matrices, discourages an acceptable approximation for both large number of nodes or flat function interpolation. In current work, a new type of basis named well–conditioned RBFs (WRBFs) were created by adding the strictly positive definite Radial Basis

In this paper, we investigate the Kaczmarz-Tanabe method for exact and inexact linear systems. The Kaczmarz-Tanabe method is derived from the Kaczmarz method, but is more stable than that. We analyze the convergence and the convergence rate of the Kaczmarz-Tanabe method based on the singular value decomposition theory, and discover two important factors, i.e., the second maximum singular value of Q

In this paper, we study spectral properties of the hypercubes, a special kind of Cayley graphs. We determine explicitly all the eigenvalues and their corresponding multiplicities of the normalized Laplacian matrix of the hypercubes by a recursive method. As applications of these results, we derive the explicit formula to the eigentime identity for random walks on the hypercubes and show that it grows

A stabilizer free weak Galerkin (WG) finite element method on polytopal mesh has been introduced in Part I of this paper (Ye and Zhang (2020)). Removing stabilizers from discontinuous finite element methods simplifies formulations and reduces programming complexity. The purpose of this paper is to introduce a new WG method without stabilizers on polytopal mesh that has convergence rates one order higher

In this paper we introduce the notion of Steklov eigenvalues for the Lamé operator in the theory of linear elasticity. In this eigenproblem the spectral parameter appears on a Robin boundary condition, linking the traction and the displacement. We investigate the spectrum of this problem and study the existence of eigenpairs on Lipschitz domains as well as show that any conforming Galerkin method is

An external barrier option has a random variable which determines whether the option is knock-in or knock-out. In this paper, we deal with the pricing of the external barrier option under a stochastic volatility model incorporated by a fast mean-reverting process. By using a singular perturbation method (asymptotic analysis) on the given partial differential equation for the option price, and applying

It is well-known that the Floater-Hormann interpolants give better results than other interpolants, especially in the case of equidistant points. In this paper, we generalize it to the Hermite case and establish a family of barycentric rational Hermite interpolants rm that do not suffer from divergence problems, unattainable points and occurrence of real poles. Furthermore, if the order m of the Hermite

Isolating the singularities of a plane curve is the first step towards computing its topology. For this, numerical methods are efficient but not certified in general. We are interested in developing certified numerical algorithms for isolating the singularities. In order to do so, we restrict our attention to the special case of plane curves that are projections of smooth curves in higher dimensions

This paper describes a new method to calculate the stationary scattering matrix and its derivatives for Euclidean waveguides. This is an adaptation and extension to a procedure developed by Levitin and Strohmaier which was used to compute the stationary scattering matrix on surfaces with hyperbolic cusps (Levitin and Strohmaier, 2019), but limited to those surfaces. At the time of writing, these procedures

In September of 2020, Arctic sea ice extent was the second-lowest on record. State of the art climate prediction uses Earth system models (ESMs), driven by systems of differential equations representing the laws of physics. Previously, these models have tended to underestimate Arctic sea ice loss. The issue is grave because accurate modeling is critical for economic, ecological, and geopolitical planning

The problems of recovering a multivariate function f from the scaled values of its Laplace and Radon transforms are studied, and two novel methods for approximating and estimating the unknown function are proposed. Moreover, using the empirical counterparts of the Laplace transform of the underlying function, a new estimate of the Radon transform itself is obtained. Under smoothed conditions on the

In this paper, we consider the regularization of the backward problem of diffusion process with time-fractional derivative. Since the equation under consideration involves the time-fractional derivative, we introduce a new perturbation which is related to the time-fractional derivative into the original equation. This leads to a fractional-order quasi-reversibility method. In theory, we give the regularity

In recent papers (see e.g. Ruas (2020a) and Ruas (2020b)) a nonparametric technique of the Petrov–Galerkin type was analyzed, whose aim is the accuracy enhancement of higher order finite element methods to solve boundary value problems with Dirichlet conditions, posed in smooth curved domains. In contrast to parametric elements, it employs straight-edged triangular or tetrahedral meshes fitting the

Free vibration characteristics of thin perforated shells of revolution vary depending not only on the dimensionless thickness of the shell but also on the perforation structure. All holes are assumed to be free, that is, without any kinematical constraints. For a given configuration there exists a critical value of the dimensionless thickness below which homogenisation fails, since the modes do not

This report considers a variable time-stepping algorithm proposed by Dahlquist, Liniger and Nevanlinna and discusses its application to the unsteady Stokes/Darcy model. Although long-time forgotten and little explored, the algorithm performs advantages in variable time-stepping analysis of various fluid flow systems, including the coupled Stokes/Darcy model. We first prove that the approximate solutions

We propose an efficient iterative scheme to solve numerically a quadratic matrix equation related to the noisy Wiener–Hopf problems for Markov chains. We improve the efficiency and the accuracy of the well-known Newton’s method, frequently used in the literature. We provide a semilocal convergence result for this iterative scheme, where we establish domains of existence and uniqueness of solution.

We consider finite element discretizations for convection–diffusion problems under low regularity assumptions. The derivation and analysis use the primal–dual weak Galerkin (PDWG) finite element framework. The Euler–Lagrange formulation resulting from the PDWG scheme yields a system of equations involving not only the equation for the primal variable but also its adjoint for the dual variable. We show

This paper proposes a novel adaptive higher-order finite element (hp-FEM) method for solving elliptic eigenvalue problems, where n eigenpairs are calculated simultaneously, but on individual higher-order finite element meshes. The meshes are automatically hp-refined independently of each other, with the goal to use an optimal mesh sequence for each eigenfunction. The method and the adaptive algorithm

Acoustic waves in a poroelastic medium with periodic structure are studied with respect to permanent seepage flow which modifies the wave propagation. The effective medium model is obtained using the homogenization of the linearized fluid–structure interaction problem while respecting the advection phenomenon in the Navier–Stokes equations. For linearization of the micromodel, an acoustic approximation

This paper concerns the design of a Fourier based pseudospectral numerical method for the model of European option pricing with transaction costs under exponential utility derived by Davis, Panas and Zariphopoulou in Davis et al. (1993). Computing the option price involves solving two stochastic optimal control problems. With an exponential utility function, the dimension of the problem can be reduced

A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can be troublesome when the perfectly matched layer (PML) boundary condition is implemented. In this paper, we present a general approach for constructing fourth-order

We propose in this paper three generalized auxiliary scalar variable (G-SAV) approaches for developing, efficient energy stable numerical schemes for gradient systems. The first two G-SAV approaches allow a range of functions in the definition of the SAV variable, furthermore, the second G-SAV approach only requires the total free energy to be bounded from below as opposed to the requirement that the

A weak Galerkin (WG) finite element method without stabilizers was introduced in Ye and Zhang (2020) on polytopal mesh. Then it was improved in Ye and Zhang (2021) with order one superconvergence. The goal of this paper is to develop a new stabilizer free WG method on polytopal mesh. This method has convergence rates two orders higher than the optimal convergence rates for the corresponding WG solution

As a generalization of the well-known linear complementarity problem, tensor complementarity problem (TCP) has been studied extensively in the literature from theoretical perspective. In this paper, we consider a class of TCPs equipped with nonsingular (not necessarily symmetric) M-tensors. The considered TCPs can be regarded as a special class of nonlinear complementarity problems (NCPs), but the

In this work, we propose a multi-stage training strategy for the development of deep learning algorithms applied to problems with multiscale features. Each stage of the proposed strategy shares an (almost) identical network structure and predicts the same reduced order model of the multiscale problem. The output of the previous stage will be combined with an intermediate layer for the current stage

In this paper, we investigate European and Asian options with default risk in an intensity-based model. By breaking down the risk into idiosyncratic and systematic components, we describe the underlying asset price using a two-factor stochastic volatility model and incorporate the correlation between the underlying asset and default risk. In the proposed framework, we obtain explicit pricing formulae

This article introduces several efficient and easy-to-use tools to analyze the intersection curve between two quadrics, on the basis of the study of its projection on a plane (the so-called cutcurve) to perform the corresponding lifting correctly. This approach is based on an efficient way of determining the topology of the cutcurve through only solving one degree eight (at most) univariate equation

Whitney forms are widely known as finite elements for differential forms. Whitney’s original definition yields first order functions on simplicial complexes, and a lot of research has been devoted to extending the definition to nonsimplicial cells and higher order functions. As a result, the term Whitney forms has become somewhat ambiguous in the literature. Our aim here is to clarify the concept of

In this paper, we propose a novel numerical technique to 2D multi-term time and space fractional Bloch–Torrey equations defined on an irregular convex domain. First, we consider the problem with space integral Laplacian operator. We present the semi-discrete and fully-discrete schemes by using the L1 formula on a temporal graded mesh and an unstructured-mesh Galerkin finite element method (FEM) based

In this paper we present a variable annuity (VA) contract embedded with a guaranteed minimum accumulated benefit rider that can be chosen to surrender the contract anytime before the maturity. In contrast to the model considered by Bernard et al. (2014), the surrender benefit in our problem is linked to the maximum value between the policyholder’s account value and the guaranteed minimum accumulated

In this paper, we propose a shift-dependent uncertainty measure related to extropy. Dynamic versions of the proposed measure are also considered along with their various properties. Nonparametric estimators for the new measures are also obtained. The methods are illustrated using simulated and real data sets.

Based on the fact that the linear term is strongly dominant over the nonlinear term, by using the approximate inverse-free preconditioned conjugate gradient (AIPCG) iteration technique, we establish the Picard-AIPCG iteration method to solve Toeplitz systems of weakly nonlinear equations. Since the storage and the accurate computation of Jacobian matrix are not necessary in this method and the only

In this paper we study a stationary generalized bioconvection problem given by a Navier–Stokes type system coupled to a cell conservation equation for describing the hydrodynamic and micro-organisms concentration, respectively, of a culture fluid, assumed to be viscous and incompressible, and in which the viscosity depends on the concentration. The model is rewritten in terms of a first-order system

In this paper, we introduce a modified Krasnoselski–Mann type method for solving the hierarchical fixed point problem and split monotone variational inclusions in real Hilbert spaces. We prove that the sequence generated by the modified algorithm converges strongly to a common element of the set of hierarchical fixed point problem and split monotone variational inclusions only basing on the coefficients

Let A,B∈ℂn×n with ind(A)=k and ind(B)=s and let LB=B2B†○. A new condition (Cs,∗): R(Ak)∩N((Bs)∗)={0} and R(Bs)∩N((Ak)∗)={0}, is defined. Some new characterizations related to core-EP inverses are obtained when B satisfies condition (Cs,∗). Explicit expressions of B†○ and BB†○ are also given. In addition, equivalent conditions, which guarantee that B satisfies condition (Cs,∗), are investigated. We

The inverse problem of determining the cross-sectional area of a human vocal tract during the utterance of a vowel is considered. The frequency-dependent boundary condition at the lips is expressed in terms of the acoustic impedance of a vibrating piston on an infinite plane baffle. The corresponding pressure at the lips is expressed in terms of the normalized impedance and a key quantity related to

Zero-sum games are a well known class of game theoretic models, which are widely used in several economics and engineering applications. It is known that any two-player finite zero-sum game in mixed-strategies can be solved, i.e., one of its Nash equilibria can be found solving a linear programming problem associated to it. The idea of this work is to propose and solve zero-sum games which involve

In this paper a simplified mathematical model related to human phonation process is presented. Main attention is paid to the treatment of vocal fold vibrations excited by viscous incompressible airflow, which is stopped (chopped) by their periodical contacts. The Hertz impact model is used in the structural part and two new strategies are suggested to treat the contact phenomena in the fluid model

We consider an equilibrium problem for a 2D elastic body with a thin elastic T-shape inclusion. A part of the inclusion is delaminated from the elastic body forming a crack between the inclusion and the surrounding elastic body. Inequality type boundary conditions are imposed at the crack faces preventing interpenetration between the crack faces. The model is characterized by a damage parameter. This

We present a stabilised finite element method for the Stokes equations. The stabilisation is based on a biorthogonal system, which preserves the locality of the approach. We present a priori error estimates of the presented scheme and demonstrate some numerical results.

In this paper, a multichannel queueing network and the problem of asymptotic merging for its set of nodes are considered. Rate of input flow arriving to the network depends on time. Service times in the network nodes are generally distributed. We introduce a multivariate service process as the number of calls being processed in the nodes. Under heavy traffic conditions, functional limit theorems of