Computers & Mathematics with Applications最新文献

{"title":"Exploring Gaussian radial basis function integrals for weight generation with application in financial option pricing","authors":"Chunyu Yan","doi":"10.1016/j.camwa.2024.12.022","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.022","url":null,"abstract":"We introduce a novel numerical method via a class of radial basis function-produced finite difference solvers, applicable to both interpolation and partial differential equation (PDE) problems. The method leverages integrals of the Gaussian kernel, introducing new weights for problem-solving. Analytical solutions to approximate the derivatives of a function are derived and computed on a stencil with both non-uniform and uniform distances. Our observations indicate that the analytical weights exhibit greater stability compared to the numerical weights when addressing problems. In the final step, we use the derived formulations to solve a multi-dimensional option pricing problem in finance. The results demonstrate that our proposed numerical method outperforms in terms of numerical accuracy across grids of different sizes. Given the multi-dimensional nature of the dealing model, which involves handling a basket of assets, our approach becomes particularly relevant for assessing and managing financial risks.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"52 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Composite iteration for isogeometric collocation method using LSPIA and Schulz iteration","authors":"Gengchen Li, Hongwei Lin, Depeng Gao","doi":"10.1016/j.camwa.2024.12.026","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.026","url":null,"abstract":"The isogeometric least-squares collocation method (IGA-L) is an effective numerical technique for solving partial differential equations (PDEs), which utilizes the non-uniform rational B-splines (NURBS) to represent the numerical solution and constructs a system of equations using more collocation points than the number of unknowns. However, on the one hand, the convergence rate of the isogeometric collocation method is lower than that of the isogeometric Galerkin (IGA-G) method; on the other hand, the freedom of the numerical solution cannot be determined in advance to reach specified precision. In this paper, we model the solution of PDEs using IGA-L as a data fitting problem, in which the linear combination of the numerical solution and its derivatives is employed to fit the load function. Moreover, we develop a composite iterative method combining the least-squares progressive-iterative approximation (LSPIA) with the three-order Schulz iteration to solve the data fitting problem. The convergence of composite iterative method is proved, and the error bound is analyzed. Numerical results demonstrate that the convergence rate of the composite iterative method for IGA-L is nearly the same as that of IGA-G. Finally, we propose an incremental fitting algorithm with the composite iterative method, by which the freedom of numerical solution can be determined automatically to reach the specified fitting precision.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"2 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modified preconditioned Newton-Krylov approaches for Navier-Stokes equations using nodal integral method","authors":"Nadeem Ahmed, Suneet Singh, Ram Prakash Bharti","doi":"10.1016/j.camwa.2024.12.027","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.027","url":null,"abstract":"Nodal integral methods (NIMs) have been proven effective in solving a wide range of scientific and engineering problems by providing accurate solutions with coarser grids. Despite notable advantages, these methods have encountered limited acceptance within the fluid flow community, primarily due to the lack of robust and efficient nonlinear solvers for the algebraic equations arising from discretization using NIM. A preconditioned Jacobian-free Newton-Krylov approach has been recently developed to solve Navier-Stokes equations to overcome this limitation. The developed approach has extended the acceptability of NIM and demonstrated considerable gains in computational time. However, a challenge persists in the efficiency of the proposed approach, particularly in solving the pressure Poisson equation. Addressing this, we offer novel strategies and algorithms to solve the pressure Poisson equation. These strategies aim to improve the computational efficiency of NIMs, making them more effective in solving complex problems in scientific and engineering applications.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"37 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"MC-CDNNs: The Monte Carlo-coupled deep neural networks approach for stochastic dual-porosity-Stokes flow coupled model","authors":"Jian Li, Shaoxuan Li, Jing Yue","doi":"10.1016/j.camwa.2024.12.024","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.024","url":null,"abstract":"In this paper, we propose a coupled neural network learning method to solve the stochastic dual-porosity-Stokes flow problem. We combine Monte Carlo and coupled deep neural networks methods (MC-CDNNs) to transform the uncertain stochastic coupled problems into a deterministic coupled problem, and compile the complex interface conditions associated with the coupled problem into the neural network to guarantee the physical constraints of the approximate solution. In addition, the convergence analysis illustrates the capability of the method in solving the stochastic coupling problem. Particularly, we conducted 2D/3D numerical experiments to demonstrate the algorithm's effectiveness and efficiency, and to show its advantages in practical applications.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Understanding avascular tumor growth and drug interactions through numerical analysis: A finite element method approach","authors":"Vivek S. Yadav, Nishant Ranwan, Nagaiah Chamakuri","doi":"10.1016/j.camwa.2024.12.023","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.023","url":null,"abstract":"This article establishes the existence of a fully discrete weak solution for the tumor growth model, which is described by a coupled non-linear reaction-diffusion system. This model incorporates crucial elements such as cellular proliferation, nutrient diffusion, prostate-specific antigen, and drug effects. We employ the finite element method for spatial discretization and the implicit Euler method for temporal discretization. Firstly, we analyzed the existence and uniqueness of the fully discretized tumor growth model. Additionally, stability bounds for the fully discrete coupled system are derived. Secondly, through multiple numerical simulations utilizing higher-order finite element methods, we analyze tumor growth behavior both with and without drug interaction, yielding a more accurate numerical solution. Furthermore, we compare CPU time efficiency across different time marching methods and explore various preconditioners to optimize computational performance.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"74 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Superconvergence of triquadratic finite elements for the second-order elliptic equation with variable coefficients","authors":"Jinghong Liu","doi":"10.1016/j.camwa.2025.01.001","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.001","url":null,"abstract":"This study focuses on superconvergence of the tensor-product quadratic finite element (so-called triquadratic finite element) in a regular family of rectangular partitions of the domain for the second-order elliptic equation with variable coefficients in three dimensions. In this paper, we first introduce a variable coefficients elliptic boundary value problem and its finite elements discretization, as well as some important functions such as the discrete Green's function and discrete derivative Green's function. Then, an interpolation operator of project type is given, by which we derive a interpolation fundamental estimate (so-called weak estimate) for general variable coefficients elliptic equations. Finally, combining the weak estimate and estimates for the discrete Green's function and discrete derivative Green's function, we get superconvergence estimates for derivatives and function values of the finite element approximation in the pointwise sense of the <mml:math altimg=\"si1.svg\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>∞</mml:mo></mml:mrow></mml:msup></mml:math>-norm.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"27 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical simulation of nonlinear fractional integro-differential equations on two-dimensional regular and irregular domains: RBF partition of unity","authors":"M. Fardi, B. Azarnavid, S. Mohammadi","doi":"10.1016/j.camwa.2024.12.019","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.019","url":null,"abstract":"In this article, we introduce a numerical method that combines local radial basis functions partition of unity with backward differentiation formula to efficiently solve linear and nonlinear fractional integro-differential equations on two-dimensional regular and irregular domains. We derive the time-discretized formulation using the backward difference formula. The meshless radial basis function method, particularly the radial basis function partition of unity method, offers advantages such as flexibility, accuracy, ease of implementation, adaptive refinement, and efficient parallelization. We apply the radial basis function partition of unity method to spatially discretize the problem using the scaled Lagrangian form of polyharmonic splines as approximation bases. Numerical simulations demonstrate the efficacy of our method in solving linear and nonlinear fractional integro-differential equations with complex domains and smooth and nonsmooth initial conditions. Comparative analysis confirms the superior performance of our proposed method.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"15 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142935961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Direct sampling method for solving the inverse acoustic wave scattering problems in the time domain","authors":"Hong Guo, Jin Huang, Zhaoxing Li","doi":"10.1016/j.camwa.2024.12.018","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.018","url":null,"abstract":"Based on the direct sampling method, this paper solves the inverse acoustic wave scattering problem from the transient scattered field. Two indicator functions can be obtained to reconstruct the shapes and the locations of the unknown scatterers, including the point-like scatterers and the extended scatterers. Our reconstruction method is easy to be implement because only the integrals need to be computed for the indicator functions. The asymptotic properties of the indicator function for the point-like scatterer are proved according to the Fourier-Laplace transform. Meanwhile, the effectiveness and the robustness of our method have been illustrated from two numerical examples.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"36 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142935955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical wetting simulations using the plicRDF-isoAdvector unstructured Volume-of-Fluid (VOF) method","authors":"Muhammad Hassan Asghar, Mathis Fricke, Dieter Bothe, Tomislav Marić","doi":"10.1016/j.camwa.2024.12.015","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.015","url":null,"abstract":"Numerical simulation of wetting and dewetting of geometrically complex surfaces benefits from the boundary-fitted unstructured Finite Volume method because it discretizes boundary conditions on geometrically complex domain boundaries with second-order accuracy and simplifies the simulation workflow. The plicRDF-isoAdvector method, an unstructured geometric Volume-of-Fluid (VOF) method, reconstructs the Piecewise Linear Interface Calculation (PLIC) interface by <ce:underline>r</ce:underline>econstructing signed <ce:underline>d</ce:underline>istance <ce:underline>f</ce:underline>unctions (RDF). This method is chosen to investigate wetting processes because of its volume conservation property and high computational efficiency. The present work verifies and validates the plicRDF-isoAdvector method for wetting problems, employing five different case studies. The first study investigates the accuracy of the interface advection near walls. The method is further investigated for the spreading of droplets on a flat and a spherical surface, respectively, for which excellent agreement with the reference solutions is obtained. Furthermore, a validation study using a droplet spreading test case is carried out. The uncompensated Young stress is introduced in the contact angle boundary condition, which significantly improves the validation of the numerical method. Furthermore, a 2D capillary rise is considered, and a numerical comparison based on results from previous work is performed. A suite with all case studies, input data, and Jupyter Notebooks used in this study are publicly available to facilitate further research and comparison with other numerical codes.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"83 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Robust finite element solvers for distributed hyperbolic optimal control problems","authors":"Ulrich Langer, Richard Löscher, Olaf Steinbach, Huidong Yang","doi":"10.1016/j.camwa.2024.12.012","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.012","url":null,"abstract":"We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic distributed, tracking-type optimal control problems with both the standard <mml:math altimg=\"si1.svg\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> and the more general energy regularizations. In contrast to the usual time-stepping approach, we discretize the optimality system by space-time continuous piecewise-linear finite element basis functions which are defined on fully unstructured simplicial meshes. If we aim at the asymptotically best approximation of the given desired state <mml:math altimg=\"si2.svg\"><mml:msub><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:math> by the computed finite element state <mml:math altimg=\"si3.svg\"><mml:msub><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>ϱ</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msub></mml:math>, then the optimal choice of the regularization parameter <ce:italic>ϱ</ce:italic> is linked to the space-time finite element mesh-size <ce:italic>h</ce:italic> by the relations <mml:math altimg=\"si208.svg\"><mml:mi>ϱ</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:msup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:math> and <mml:math altimg=\"si241.svg\"><mml:mi>ϱ</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:msup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> for the <mml:math altimg=\"si1.svg\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> and the energy regularization, respectively. For this setting, we can construct robust (parallel) iterative solvers for the reduced finite element optimality systems. These results can be generalized to variable regularization parameters adapted to the local behavior of the mesh-size that can heavily change in the case of adaptive mesh refinements. The numerical results illustrate the theoretical findings firmly.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"16 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}