Pub Date : 2026-01-02DOI: 10.1016/j.aml.2025.109868
Ruisheng Qi
In this paper, we consider strong convergence of a novel fully discrete finite element approximation of stochastic PDEs with non-globally Lipschitz coefficients and multiplicative noise in space dimension . The discretization in space is the standard finite element method and the discretization in time is a tamed drift semi-implicit scheme. This scheme makes the nonlinearity be solved explicitly while being unconditionally stable. Under regularity assumptions, we establish the optimal strong convergence rates in both space and time for the considered scheme.
{"title":"Strong convergence of a fully discrete finite element approximation of non-Lipschitz SPDEs with multiplicative noise","authors":"Ruisheng Qi","doi":"10.1016/j.aml.2025.109868","DOIUrl":"10.1016/j.aml.2025.109868","url":null,"abstract":"<div><div>In this paper, we consider strong convergence of a novel fully discrete finite element approximation of stochastic PDEs with non-globally Lipschitz coefficients and multiplicative noise in space dimension <span><math><mrow><mi>d</mi><mo>≤</mo><mn>3</mn></mrow></math></span>. The discretization in space is the standard finite element method and the discretization in time is a tamed drift semi-implicit scheme. This scheme makes the nonlinearity be solved explicitly while being unconditionally stable. Under regularity assumptions, we establish the optimal strong convergence rates in both space and time for the considered scheme.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109868"},"PeriodicalIF":2.8,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894456","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}
We study the long-term multivalued random dynamical behavior for a non-autonomous Benjamin–Bona–Mahony equation on a 3D unbounded channel with a non-Lipschitz diffusion coefficient and a cubic polynomial growth vector field. Our main results are the existence of multivalued non-autonomous random dynamical systems and strongly compact random attractors in . Such results for quadratic polynomial vector fields have been proved by Chen, Wang, Wang and Zhang (Math. Ann, 386 (2023) 343–373) and Chen, Wang and Zhang (SIAM J. Math. Anal. 56 (2024) 254–274) by the spectral decomposition method. In this paper, we prove that such results are also valid for a weak integrability condition on the time-dependent external forcing and the polynomial vector fields of cubic growth which involving a critical Sobolev embedding. The famous energy balance equation method developed by Ball (Discrete Contin. Dyn. Syst., 10 (2004) 31–52) is used to deal with the non-compact embedding problems and the non-applicability of the spectral decomposition method for cubic polynomial vector fields.
{"title":"Multivalued random dynamics of colored noise driven BBM equations on 3D unbounded channels with cubic polynomial vector fields","authors":"Ruiyi Xu, Linsong Chen, Liguang Zhou, Xuping Zhang","doi":"10.1016/j.aml.2025.109869","DOIUrl":"10.1016/j.aml.2025.109869","url":null,"abstract":"<div><div>We study the long-term multivalued random dynamical behavior for a non-autonomous Benjamin–Bona–Mahony equation on a 3D unbounded channel with a <em>non-Lipschitz diffusion coefficient</em> and a <em>cubic polynomial growth vector field</em>. Our main results are the existence of multivalued non-autonomous random dynamical systems and strongly compact random attractors in <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup></math></span>. Such results for <em>quadratic polynomial vector fields</em> have been proved by Chen, Wang, Wang and Zhang (Math. Ann, 386 (2023) 343–373) and Chen, Wang and Zhang (SIAM J. Math. Anal. 56 (2024) 254–274) by the spectral decomposition method. In this paper, we prove that such results are also valid for a weak integrability condition on the time-dependent external forcing and the polynomial vector fields of <em>cubic</em> growth which involving a <em>critical</em> Sobolev embedding. The famous energy balance equation method developed by Ball (Discrete Contin. Dyn. Syst., 10 (2004) 31–52) is used to deal with the non-compact embedding problems and the non-applicability of the spectral decomposition method for cubic polynomial vector fields.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109869"},"PeriodicalIF":2.8,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894455","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}
Pub Date : 2025-12-30DOI: 10.1016/j.aml.2025.109861
Seung-Yeal Ha , Jaemoon Lee , Qinghua Xiao , Fanqin Zeng
We study the weak flocking of the Cucker–Smale–Fokker–Planck (in short, CS–FP) equation with a degenerate diffusion coefficient. When the communication weight function has a positive lower bound, weak flocking occurs asymptotically. In contrast, when the communication weight function tend to zero, it is not known whether weak flocking occurs or not. In this paper, we revisit this delicate situation in which the communication weight function tends to zero at infinity and the noise amplitude also decays to zero sufficiently fast. To bypass the difficulty, we use the method of effective domain by identifying a time-varying region in which the total mass outside of it decays to zero sufficiently fast. Moreover, we show that if the communication weight function and the noise amplitude both have a suitable polynomial decay, then weak flocking occurs.
我们研究了具有简并扩散系数的cucker - small - fokker - planck（简称CS-FP）方程的弱群。当通信权函数的下界为正时，渐近出现弱簇。相反，当通信权函数趋于零时，不知道是否发生弱群集。在本文中，我们重新审视了这种微妙的情况，即通信权函数在无穷远处趋于零，噪声幅度也足够快地衰减到零。为了克服这个困难，我们使用有效域的方法，通过确定一个时变区域，在该区域外的总质量衰减到零的速度足够快。此外，我们还证明了如果通信权函数和噪声幅值都有合适的多项式衰减，则会发生弱群集。
{"title":"A priori estimates on the weak flocking of the Cucker–Smale–Fokker–Planck equation","authors":"Seung-Yeal Ha , Jaemoon Lee , Qinghua Xiao , Fanqin Zeng","doi":"10.1016/j.aml.2025.109861","DOIUrl":"10.1016/j.aml.2025.109861","url":null,"abstract":"<div><div>We study the weak flocking of the Cucker–Smale–Fokker–Planck (in short, CS–FP) equation with a degenerate diffusion coefficient. When the communication weight function has a positive lower bound, weak flocking occurs asymptotically. In contrast, when the communication weight function tend to zero, it is not known whether weak flocking occurs or not. In this paper, we revisit this delicate situation in which the communication weight function tends to zero at infinity and the noise amplitude also decays to zero sufficiently fast. To bypass the difficulty, we use the method of effective domain by identifying a time-varying region in which the total mass outside of it decays to zero sufficiently fast. Moreover, we show that if the communication weight function and the noise amplitude both have a suitable polynomial decay, then weak flocking occurs.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109861"},"PeriodicalIF":2.8,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894474","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}
Pub Date : 2025-12-30DOI: 10.1016/j.aml.2025.109860
Ahmed Alsaedi , Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu
We consider a nonlinear Dirichlet problem with gradient dependence. The features of this paper are twofold: (i) the problem is driven by a general nonlinear nonhomogeneous differential operator with Uhlenbeck–Lieberman structure; (ii) the reaction blows-up at the origin and it is gradient dependent. Using a topological approach based on fixed point theory, we show that for all small values of there are “eigenvalues” of the problem with smooth corresponding eigenfunctions.
{"title":"Small perturbations of convective singular eigenvalue problems","authors":"Ahmed Alsaedi , Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu","doi":"10.1016/j.aml.2025.109860","DOIUrl":"10.1016/j.aml.2025.109860","url":null,"abstract":"<div><div>We consider a nonlinear Dirichlet problem with gradient dependence. The features of this paper are twofold: (i) the problem is driven by a general nonlinear nonhomogeneous differential operator with Uhlenbeck–Lieberman structure; (ii) the reaction blows-up at the origin and it is gradient dependent. Using a topological approach based on fixed point theory, we show that for all small values of <span><math><mrow><mi>λ</mi><mo>></mo><mn>0</mn></mrow></math></span> there are “eigenvalues” of the problem with smooth corresponding eigenfunctions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109860"},"PeriodicalIF":2.8,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894475","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}
Pub Date : 2025-12-27DOI: 10.1016/j.aml.2025.109859
Andreea Gruie, Călin Şerban
We prove that, for any continuous , the non-homogeneous discrete Dirichlet problem where is a potential homeomorphism, is solvable iff . Our approach relies on the Legendre–Fenchel transform and Brouwer’s fixed point theorem.
{"title":"Non-homogeneous discrete Dirichlet problem with singular ϕ-Laplacian","authors":"Andreea Gruie, Călin Şerban","doi":"10.1016/j.aml.2025.109859","DOIUrl":"10.1016/j.aml.2025.109859","url":null,"abstract":"<div><div>We prove that, for any continuous <span><math><mrow><mi>f</mi><mo>:</mo><mi>Z</mi><mrow><mo>[</mo><mn>1</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>×</mo><msup><mrow><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo></mrow></mrow><mrow><mi>T</mi></mrow></msup><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span>, the non-homogeneous discrete Dirichlet problem <span><math><mrow><mi>Δ</mi><mrow><mo>[</mo><mi>ϕ</mi><mrow><mo>(</mo><mi>Δ</mi><mi>u</mi><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>)</mo></mrow><mo>]</mo></mrow><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>u</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>,</mo><mo>…</mo><mo>,</mo><mi>u</mi><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow><mo>)</mo></mrow><mspace></mspace><mrow><mo>(</mo><mi>n</mi><mo>∈</mo><mi>Z</mi><mrow><mo>[</mo><mn>1</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>)</mo></mrow><mo>;</mo><mspace></mspace><mi>u</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><mi>A</mi><mo>,</mo><mi>u</mi><mrow><mo>(</mo><mi>T</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>=</mo><mi>B</mi><mo>,</mo></mrow></math></span> where <span><math><mrow><mi>ϕ</mi><mo>:</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span> is a potential homeomorphism, is solvable iff <span><math><mrow><mrow><mo>|</mo><mi>A</mi><mo>−</mo><mi>B</mi><mo>|</mo></mrow><mo><</mo><mrow><mo>(</mo><mi>T</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mi>a</mi></mrow></math></span>. Our approach relies on the Legendre–Fenchel transform and Brouwer’s fixed point theorem.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109859"},"PeriodicalIF":2.8,"publicationDate":"2025-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145845079","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}
Pub Date : 2025-12-26DOI: 10.1016/j.aml.2025.109857
Minh-Phuong Tran , Thanh-Nhan Nguyen
We study the regularity of solutions to nonlinear elliptic equations of -Laplace type modeled from composite materials. The main difficulty comes from the geometric structures of the composite, specifically the disjoint Reifenberg flat subdomains , their boundaries , and the BMO smallness properties of each tensor coefficient that pose significant challenges. In this paper, we develop a novel free-scaling approach to establish the local decay estimates for level sets of the gradient of the weak solutions. This approach is of independent technical interest, and it is flexible enough to be applied for deriving improved gradient regularity in a larger class of rearrangement-invariant function spaces.
{"title":"Global Marcinkiewicz estimates for p-Laplace equations in composite media: A new free-scaling approach via distribution functions","authors":"Minh-Phuong Tran , Thanh-Nhan Nguyen","doi":"10.1016/j.aml.2025.109857","DOIUrl":"10.1016/j.aml.2025.109857","url":null,"abstract":"<div><div>We study the regularity of solutions to nonlinear elliptic equations of <span><math><mi>p</mi></math></span>-Laplace type modeled from composite materials. The main difficulty comes from the geometric structures of the composite, specifically the disjoint Reifenberg flat subdomains <span><math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span>, their boundaries <span><math><mrow><mi>∂</mi><msub><mrow><mi>Ω</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></math></span>, and the BMO smallness properties of each tensor coefficient <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span> that pose significant challenges. In this paper, we develop a novel free-scaling approach to establish the local decay estimates for level sets of the gradient of the weak solutions. This approach is of independent technical interest, and it is flexible enough to be applied for deriving improved gradient regularity in a larger class of rearrangement-invariant function spaces.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109857"},"PeriodicalIF":2.8,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840626","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}
Pub Date : 2025-12-26DOI: 10.1016/j.aml.2025.109858
João Marcos do Ó , José Carlos de Albuquerque , Hugo H.C. Silva
This work establishes a lower bound for the Morse index of radial nodal solutions for a general class of gradient-type elliptic systems. By relating the Morse index to the negative eigenvalues of the associated linearized operator, we construct a set of non-radial eigenfunctions to find negative directions for the quadratic form. The main result shows the Morse index is bounded from below by , where and are the number of nodal domains of the solutions. Furthermore, this work explores how the estimate for the Morse index influences the structural properties of radial and nodal solutions.
{"title":"A lower bound for the Morse index of nodal radial solutions for gradient elliptic systems","authors":"João Marcos do Ó , José Carlos de Albuquerque , Hugo H.C. Silva","doi":"10.1016/j.aml.2025.109858","DOIUrl":"10.1016/j.aml.2025.109858","url":null,"abstract":"<div><div>This work establishes a lower bound for the Morse index of radial nodal solutions for a general class of gradient-type elliptic systems. By relating the Morse index to the negative eigenvalues of the associated linearized operator, we construct a set of non-radial eigenfunctions to find negative directions for the quadratic form. The main result shows the Morse index <span><math><mrow><mi>m</mi><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></mrow></math></span> is bounded from below by <span><math><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>r</mi><mi>a</mi><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mi>N</mi><mrow><mo>(</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mi>N</mi><mrow><mo>(</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, where <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> are the number of nodal domains of the solutions. Furthermore, this work explores how the estimate for the Morse index influences the structural properties of radial and nodal solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109858"},"PeriodicalIF":2.8,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145845495","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}
Pub Date : 2025-12-24DOI: 10.1016/j.aml.2025.109856
Dongxiu Wang, Anmin Mao
This paper investigates the global boundedness of solutions to a mosquito-borne disease system with chemotaxis via new approach. More specifically, by means of the loop arguments, we prove the existence of a unique globally bounded classical solution to the system without any constraint on initial data in any spatial dimension. This result generalizes some relevant results.
{"title":"Global solvability in a mosquito-borne disease system with chemotaxis","authors":"Dongxiu Wang, Anmin Mao","doi":"10.1016/j.aml.2025.109856","DOIUrl":"10.1016/j.aml.2025.109856","url":null,"abstract":"<div><div>This paper investigates the global boundedness of solutions to a mosquito-borne disease system with chemotaxis via new approach. More specifically, by means of the loop arguments, we prove the existence of a unique globally bounded classical solution to the system without any constraint on initial data in any spatial dimension. This result generalizes some relevant results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109856"},"PeriodicalIF":2.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822949","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}
Pub Date : 2025-12-23DOI: 10.1016/j.aml.2025.109855
Huiling Du , Fang Li , Bo Xue
A new nonlinear super vector equation is obtained according to a matrix spectral problem with the help of the compatibility condition. When , the corresponding hierarchy of equations is deduced and its Hamiltonian structures are constructed by means of the supertrace identity. Then an -component super CH equation is gained from a negative flow associated with the original matrix spectral problem, which admits exact solutions with -peakons, and a super dynamical system that the potentials evolve with is derived. Moreover, the infinitely many conservation laws of the -component super CH equation are discussed.
{"title":"An n-component super Camassa–Holm equation with N-peakons","authors":"Huiling Du , Fang Li , Bo Xue","doi":"10.1016/j.aml.2025.109855","DOIUrl":"10.1016/j.aml.2025.109855","url":null,"abstract":"<div><div>A new nonlinear super vector equation is obtained according to a <span><math><mrow><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mo>×</mo><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> matrix spectral problem with the help of the compatibility condition. When <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math></span>, the corresponding hierarchy of equations is deduced and its Hamiltonian structures are constructed by means of the supertrace identity. Then an <span><math><mi>n</mi></math></span>-component super CH equation is gained from a negative flow associated with the original matrix spectral problem, which admits exact solutions with <span><math><mi>N</mi></math></span>-peakons, and a super dynamical system that the potentials evolve with is derived. Moreover, the infinitely many conservation laws of the <span><math><mi>n</mi></math></span>-component super CH equation are discussed.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109855"},"PeriodicalIF":2.8,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822954","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}
Pub Date : 2025-12-19DOI: 10.1016/j.aml.2025.109854
Tongtong Sun , Fajie Wang , Xingxing Yue
This paper presents a novel local semi-analytical meshless method, based on the fundamental solutions, for acoustic eigenfrequency and modal analysis in complex two- and three-dimensional domains. The proposed approach requires only a set of discrete nodes distributed within the domain and along its boundary, thereby eliminating the need for mesh generation. By combining the moving least squares approximation with spline weight functions, locally supported coefficient matrices are constructed. The eigenfrequencies and modes are then obtained through the singular value decomposition. This local strategy effectively mitigates numerical instability, addresses the ill-conditioning issues commonly encountered in traditional global meshless methods, and avoids the mesh dependency inherent in the finite element method. Numerical experiments on both two- and three-dimensional cases demonstrate that the proposed method achieves higher computational accuracy compared to the conventional approaches, particularly in capturing high-frequency modal characteristics. The results highlight its potential as an efficient and robust tool for vibration and noise analysis in complex acoustic structures.
{"title":"A novel local semi-analytical meshless method for acoustic eigenfrequency and modal analysis","authors":"Tongtong Sun , Fajie Wang , Xingxing Yue","doi":"10.1016/j.aml.2025.109854","DOIUrl":"10.1016/j.aml.2025.109854","url":null,"abstract":"<div><div>This paper presents a novel local semi-analytical meshless method, based on the fundamental solutions, for acoustic eigenfrequency and modal analysis in complex two- and three-dimensional domains. The proposed approach requires only a set of discrete nodes distributed within the domain and along its boundary, thereby eliminating the need for mesh generation. By combining the moving least squares approximation with spline weight functions, locally supported coefficient matrices are constructed. The eigenfrequencies and modes are then obtained through the singular value decomposition. This local strategy effectively mitigates numerical instability, addresses the ill-conditioning issues commonly encountered in traditional global meshless methods, and avoids the mesh dependency inherent in the finite element method. Numerical experiments on both two- and three-dimensional cases demonstrate that the proposed method achieves higher computational accuracy compared to the conventional approaches, particularly in capturing high-frequency modal characteristics. The results highlight its potential as an efficient and robust tool for vibration and noise analysis in complex acoustic structures.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109854"},"PeriodicalIF":2.8,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784748","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}
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