Journal of Scientific Computing最新文献

{"title":"Linearly Implicit Finite Element Methods Approximating the Solution to the Nonlinear Schrödinger Equation with a Schamel-Type Nonlinearity.","authors":"Panagiotis Paraschis, Georgios E Zouraris","doi":"10.1007/s10915-026-03328-2","DOIUrl":"https://doi.org/10.1007/s10915-026-03328-2","url":null,"abstract":"<p><p>We consider an initial- and Dirichlet boundary- value problem for a nonlinear Schrödinger equation of the form <math> <mrow><msub><mi>u</mi> <mi>t</mi></msub> <mo>=</mo> <mspace></mspace> <mtext>i</mtext> <mspace></mspace> <mi>Δ</mi> <mi>u</mi> <mo>+</mo> <mtext>i</mtext> <mspace></mspace> <mi>V</mi> <mspace></mspace> <mi>u</mi> <mo>+</mo> <mtext>i</mtext> <mspace></mspace> <mi>μ</mi> <mspace></mspace> <msup><mrow><mo>|</mo> <mi>u</mi> <mo>|</mo></mrow> <mi>β</mi></msup> <mspace></mspace> <mi>u</mi> <mo>+</mo> <mi>f</mi></mrow> </math> over <math><mrow><mo>[</mo> <mn>0</mn> <mo>,</mo> <mi>T</mi> <mo>]</mo> <mo>×</mo> <mi>Ω</mi></mrow> </math> , where <math><mrow><mi>T</mi> <mo>></mo> <mn>0</mn></mrow> </math> , <math><mrow><mi>Ω</mi> <mo>⊂</mo> <msup><mrow><mi>R</mi></mrow> <mi>d</mi></msup> </mrow> </math> for <math><mrow><mi>d</mi> <mo>∈</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>}</mo></mrow> </math> , <math><mrow><mi>β</mi> <mo>∈</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo></mrow> </math> , <i>V</i> is a real-valued time-independent potential and <math><mi>μ</mi></math> is a nonzero real number. The solution to the problem is approximated by the Linearized Backward Euler finite element (LBEFE) method which is dissipative and the Linearized Crank-Nicolson finite element (LCNFE) one which is conservative. Letting <math><mi>τ</mi></math> be the time-step and <i>h</i> be the width of the finite element partition of the space domain, we provide an optimal order <math><mrow><mi>O</mi> <mo>(</mo> <mi>τ</mi> <mo>+</mo> <msup><mi>h</mi> <mn>2</mn></msup> <mo>)</mo></mrow> </math> error estimate in the <math><msup><mi>L</mi> <mn>2</mn></msup> </math> norm for both methods, and an <math><mrow><mi>O</mi> <mo>(</mo> <msup><mi>τ</mi> <mi>α</mi></msup> <mo>+</mo> <mi>h</mi> <mo>)</mo></mrow> </math> error estimate in the <math><msup><mi>H</mi> <mn>1</mn></msup> </math> norm, where <math><mrow><mi>α</mi> <mo>=</mo> <mfrac><mn>3</mn> <mn>4</mn></mfrac> </mrow> </math> in the (LBEFE) method and <math><mrow><mi>α</mi> <mo>=</mo> <mfrac><mn>1</mn> <mn>2</mn></mfrac> </mrow> </math> in the (LCNFE) one. For <math><mrow><mi>d</mi> <mo>=</mo> <mn>1</mn></mrow> </math> , no CFL conditions are imposed, while for <math><mrow><mi>d</mi> <mo>=</mo> <mn>2</mn></mrow> </math> or 3, a mesh condition of the form <math> <mrow><mrow><mo>(</mo></mrow> <msup><mi>h</mi> <mfrac><mrow><mn>2</mn> <mo>-</mo> <mi>d</mi></mrow> <mn>2</mn></mfrac> </msup> <mspace></mspace> <msup><mrow><mo>|</mo> <mo>ln</mo> <mrow><mo>(</mo> <mi>h</mi> <mo>)</mo></mrow> <mo>|</mo></mrow> <mfrac><mrow><mi>d</mi> <mo>-</mo> <mn>1</mn></mrow> <mi>d</mi></mfrac> </msup> <mspace></mspace> <msup><mi>τ</mi> <mi>α</mi></msup> <mo>+</mo> <msup><mi>h</mi> <mrow><mn>2</mn> <mo>-</mo> <mfrac><mi>d</mi> <mn>2</mn></mfrac> </mrow> </msup> <mrow><mo>)</mo></mrow> <mo>=</mo> <mi>O</mi> <mrow><mo>(</mo> <mn>1</mn> <mo>)</mo></mrow> </mrow> </math> is required. Finally,","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"108 1","pages":"15"},"PeriodicalIF":3.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13201312/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148043977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fully Well-Balanced Methods for Schwarzschild-Euler Equation in Gullstrand-Painlevé Coordinates.","authors":"Ernesto Pimentel-García, Samuel Santos-Pérez, Isabel Cordero-Carrión, Carlos Parés","doi":"10.1007/s10915-026-03324-6","DOIUrl":"10.1007/s10915-026-03324-6","url":null,"abstract":"<p><p>We present a comprehensive formulation of the general-relativistic Euler equations in Gullstrand-Painlevé coordinates, providing a description of fluid dynamics that remains regular across the Schwarzschild event horizon. After establishing the system and examining its mathematical properties including well-posedness behaviour, Riemann invariants, and characteristic wave speeds, we obtain its stationary solutions in implicit form and analyze them in detail for a representative equation of state. Building on these results, we design high-order exactly well-balanced numerical schemes capable of preserving all stationary states of the system. Both first- and second-order methods are constructed. Extensive numerical experiments confirm the accuracy, robustness, and well-balanced behavior of the proposed schemes. The study offers both theoretical insight into relativistic fluid flows near black holes and practical tools for reliable long-term simulations in curved spacetimes.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"108 1","pages":"11"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13194268/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148018558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some New Properties of an Active Flux Type Scheme: PamPa.","authors":"Rémi Abgrall, Yongle Liu, Philipp Öffner","doi":"10.1007/s10915-026-03377-7","DOIUrl":"10.1007/s10915-026-03377-7","url":null,"abstract":"<p><p>In this paper, we provide a few new properties of Active Flux (AF)/Point-Average-Moment PolynomiAl-interpreted (PamPa) schemes. First, we show, in full generality, that the AF/PamPa schemes can be interpreted in such a way that the discontinuous Galerkin (dG) scheme is one of their building blocks. Secondly we provide intrinsic bound preserving properties of the current variant of PamPa. This is also illustrated numerically. Last, we show, at least in one dimension, that the PamPa scheme has the summation by part (SBP) property.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"108 2","pages":"61"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13323264/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148377764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stochastic Conformal Integrators for Linearly Damped Stochastic Poisson Systems.","authors":"Charles-Edouard Bréhier, David Cohen, Yoshio Komori","doi":"10.1007/s10915-025-03097-4","DOIUrl":"https://doi.org/10.1007/s10915-025-03097-4","url":null,"abstract":"<p><p>We propose and study conformal integrators for linearly damped stochastic Poisson systems. We analyse the qualitative and quantitative properties of these numerical integrators: preservation of dynamics of certain Casimir and Hamiltonian functions, almost sure bounds of the numerical solutions, and strong and weak rates of convergence under appropriate conditions. These theoretical results are illustrated with several numerical experiments on, for example, the linearly damped free rigid body with random inertia tensor or the linearly damped stochastic Lotka-Volterra system.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"106 1","pages":"17"},"PeriodicalIF":3.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12672609/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145679165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Robust Finite Element Method for Linearized Magnetohydrodynamics on General Domains.","authors":"L Beirão da Veiga, C Lovadina, M Trezzi","doi":"10.1007/s10915-026-03291-y","DOIUrl":"https://doi.org/10.1007/s10915-026-03291-y","url":null,"abstract":"<p><p>We generalize and improve the finite element method for linearized Magnetohydrodynamics introduced in (Beirão da Veiga et al., SIAM J. Numer. Anal. <b>62</b>(4):1539-1564 (2024)). The main novelty is that the proposed scheme is able to handle also non-convex domains and less regular solutions. The method is proved to be pressure robust and quasi-robust with respect to both fluid and magnetic Reynolds numbers. A set of numerical tests confirms our theoretical findings.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"107 2","pages":"73"},"PeriodicalIF":3.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13070083/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147678167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiharmonic Algorithms for Contrast-Enhanced Ultrasound.","authors":"Vanja Nikolić, Teresa Rauscher","doi":"10.1007/s10915-026-03247-2","DOIUrl":"10.1007/s10915-026-03247-2","url":null,"abstract":"<p><p>Harmonic generation plays a crucial role in contrast-enhanced ultrasound, both for imaging and therapeutic applications. However, accurately capturing these nonlinear effects is computationally demanding when using traditional time-domain approaches. To address this issue, we develop algorithms based on a time discretization that uses a multiharmonic Ansatz applied to a model that couples the Westervelt equation for acoustic pressure with a volume-based approximation of the Rayleigh-Plesset equation for the dynamics of microbubble contrast agents. We first rigorously establish the existence of time-periodic solutions for this Westervelt-ODE system. We then derive a multiharmonic representation of the system under time-periodic excitation and develop iterative algorithms that rely on the successive computation of higher harmonics assuming either real-valued or complex-valued solution fields. In the real-valued setting, we characterize the approximation error in terms of the number of harmonics and a contribution arising from the fixed-point iteration. Finally, we investigate these algorithms numerically and illustrate how the number of harmonics and the presence of microbubbles influence the propagation of acoustic waves.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"107 2","pages":"41"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13013266/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147522321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inf-sup stable space-time Local Discontinuous Galerkin method for the heat equation.","authors":"Sergio Gómez, Chiara Perinati, Paul Stocker","doi":"10.1007/s10915-025-03121-7","DOIUrl":"https://doi.org/10.1007/s10915-025-03121-7","url":null,"abstract":"<p><p>We propose and analyze a space-time Local Discontinuous Galerkin method for the approximation of the solution to parabolic problems. The method allows for very general discrete spaces and prismatic space-time meshes. Existence and uniqueness of a discrete solution are shown by means of an inf-sup condition, whose proof does not rely on polynomial inverse estimates. Moreover, for piecewise polynomial spaces satisfying an additional mild condition, we show a second inf-sup condition that provides additional control over the time derivative of the discrete solution. We derive <i>hp</i>-<i>a priori</i> error bounds based on these inf-sup conditions, which we use to prove convergence rates for standard, tensor-product, and quasi-Trefftz polynomial spaces. Numerical experiments validate our theoretical results.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"106 1","pages":"22"},"PeriodicalIF":3.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12680886/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145702683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inf-Sup Stable Space-Time Discretization of the Wave Equation Based on a First-Order-In-Time Variational Formulation.","authors":"Matteo Ferrari, Ilaria Perugia, Enrico Zampa","doi":"10.1007/s10915-026-03293-w","DOIUrl":"https://doi.org/10.1007/s10915-026-03293-w","url":null,"abstract":"<p><p>In this paper, we present a conforming space-time discretization of the wave equation based on a first-order-in-time variational formulation. Our method extends the scheme of French and Peterson (1996), incorporating exponential weights in time, which yield an inf-sup stability condition for arbitrary choices of discrete subspaces, including spline spaces, without restrictions on the mesh size or time step. Moreover, using elliptic projections, we derive optimal convergence rates in both the energy and <math><msup><mi>L</mi> <mn>2</mn></msup> </math> norms for sufficiently smooth solutions and for any choice of space-time tensor product subspaces satisfying standard approximation assumptions. Numerical examples are provided to support the theoretical findings.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"107 3","pages":"89"},"PeriodicalIF":3.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13139272/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147845522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Matrix-Free Inexact Preconditioning Techniques for Isogeometric Tensor-Product Discretizations.","authors":"Michał Ł Mika, René R Hiemstra, Dominik Schillinger","doi":"10.1007/s10915-026-03253-4","DOIUrl":"https://doi.org/10.1007/s10915-026-03253-4","url":null,"abstract":"<p><p>We propose a matrix-free inexact preconditioning strategy for elliptic partial differential equations discretized by the isogeometric Galerkin method on tensor-product spline spaces. We base our preconditioner on an approximation of the discrete linear operator by a sum of Kronecker product matrices. The action of its inverse on a vector of coefficients is approximated by an inner preconditioned conjugate gradient solve. The forward problem is solved by the inexact preconditioned conjugate gradient method. The complexity of the Kronecker matrix-vector products in the inner iteration is lower than the complexity of the matrix-vector products in the forward problem, leading to a reduced number of iterations and significant performance gains. We show the robustness, efficiency and effectiveness of our approach in test problems involving the Poisson equation and linear elasticity, and illustrate the performance gain with respect to preconditioning techniques based on fast diagonalization. The proposed method is implemented in our open-source Julia framework for spline based discretization methods.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"107 3","pages":"81"},"PeriodicalIF":3.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13121230/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147787376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fast Numerical Solvers for Parameter Identification Problems in Mathematical Biology.","authors":"Karolína Benková, John W Pearson, Mariya Ptashnyk","doi":"10.1007/s10915-025-03170-y","DOIUrl":"10.1007/s10915-025-03170-y","url":null,"abstract":"<p><p>In this paper, we consider effective discretization strategies and iterative solvers for nonlinear PDE-constrained optimization models of pattern evolution within biological processes. Upon a Sequential Quadratic Programming linearization of the optimization problem, we devise appropriate time-stepping schemes and discrete approximations of the cost functionals such that the discretization and optimization operations are commutative, a highly desirable property of a discretization of such problems. We formulate the large-scale, coupled linear systems in such a way that efficient preconditioned iterative methods can be applied within a Krylov subspace solver. Numerical experiments demonstrate the viability and efficiency of our approach.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"107 1","pages":"24"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12992359/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147482075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}