Article
Mathematics, Applied
John P. Ryan, Anil Damle
Summary: This paper introduces a general method of applying hierarchical matrix skeletonization factorizations to numerical solutions of boundary integral equations, particularly useful for possibly rank-deficient operators and multiple boundary component problems. The method retains locality, allows parallelized implementation, and efficiently handles boundary geometric perturbations.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Hiroyuki Miyoshi, Darren G. Crowdy
Summary: A generalization of the Schwarz integral formula in multiply connected circular domains is proposed in this paper. In the case where the real part is given on the boundary, a classical Schwarz integral formula can recover an analytic function, and Poisson integral formulas are well-known examples for simply connected domains. The generalized integral formulas derived in this paper can retrieve an analytic function given more general linear combinations of its real and imaginary parts on each boundary component of a multiply connected domain. By combining these formulas with radial-slit conformal mappings, integral expressions for analytic functions can be obtained where more general linear combinations of their real and imaginary parts are specified on the boundary components of a multiply connected domain. These expressions are referred to as generalized Schwarz integral formulas. The usefulness and versatility of these formulas are demonstrated through applications to three topical problems: finding the potential around periodic interdigitated electrodes, solving the free boundary problem for hollow vortex wakes behind a bluff body, and determining the two-phase flow over a liquid-infused surface.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Tuomas Orponen, Michele Villa
Summary: This paper investigates the sub-elliptic problems in flag domains and their boundaries in R-3. By utilizing the sub-elliptic single and double layer potentials, we solve the Dirichlet and Neumann problems and obtain improved regularity for the solutions with certain regularity of the boundary values.
ADVANCES IN CALCULUS OF VARIATIONS
(2023)
Article
Multidisciplinary Sciences
Christopher C. Green, Marie A. Snipes, Lesley A. Ward, Darren G. Crowdy
Summary: The harmonic-measure distribution function, or h-function, is crucial for understanding the behavior of Brownian particles in planar domains. Previous research has focused on simply connected domains, but this study introduces a new calculation method and extends it to doubly and multiply connected domains, resulting in satisfactory results.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Mathematics
Ali W. K. Sangawi, Ali H. M. Murid, Khiy Wei Lee
Summary: This paper introduces a fast boundary integral equation method for numerical conformal mapping and its inverse, which can handle regions with complex geometry and high connectivity. The complexity of this method is lower compared to previous algorithms, and it shows potential applications in medical human brain image processing.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2021)
Article
Mathematics, Applied
Daniel Faraco, Sauli Lindberg, David MacTaggart, Alberto Valli
Summary: In this letter, the proof by Faraco and Lindberg (2020) of Taylor's conjecture in multiply connected domains is extended to include arbitrary vector potentials and remove the need for restrictions on the magnetic field to ensure gauge invariance of the helicity integral. This extension allows for the treatment of general magnetic fields in closed domains, closing a conjecture that has been open for almost 50 years.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Computer Science, Software Engineering
Dongbo Shi, Renjie Chen
Summary: Shape interpolation is a fundamental problem in computer graphics. This paper proposes an interpolation scheme for harmonic mappings that specifically addresses the limitation of applying interpolation methods to shapes within multiply-connected domains. By projecting the interpolated metric into the planar harmonic mapping space and using a Newton iteration, the isometric distortion of the intermediate mapping is minimized. Additionally, a simple analytic formula for the positive semidefinite (PSD) projection of the Hessian matrix is derived for more efficient iteration. Extensive experiments and comparisons with state-of-the-art methods demonstrate the efficacy and robustness of the proposed method.
COMPUTER GRAPHICS FORUM
(2022)
Article
Mathematics
Yanjun Ma
Summary: In this paper, we study a zeroth-order perturbation q(x) of the buckling operator delta(2)-kappa delta, and show that it can be uniquely determined by measuring the Dirichlet-to-Neumann data on the boundary. We extend the conclusion of the biharmonic operator to the buckling operator, and the Dirichlet-to-Neumann map provided in this study is more meaningful and general.
Article
Mathematics, Applied
Yu. M. Sybil
Summary: This paper discusses Dirichlet and Neumann boundary value problems for the two-dimensional Laplace equation in a multiply-connected domain enclosed by two smooth closed curves. The solutions are presented as a sum of potentials of double layer with unknown densities, and existence and uniqueness of solutions in appropriate functional spaces are proved. By using integral representation of solutions, systems of boundary integral and singular integro-differential equations are obtained, and a modified system of boundary equations with unique solutions is considered to determine densities of the solutions satisfying additional integral conditions.
JOURNAL OF NUMERICAL AND APPLIED MATHEMATICS
(2021)
Article
Engineering, Multidisciplinary
Luiz M. Faria, Carlos Perez-Arancibia, Marc Bonnet
Summary: This paper introduces a general high-order kernel regularization technique that can be applied to linear elliptic PDEs in two and three spatial dimensions. By interpolating the density function and solutions of the underlying homogeneous PDE, singular and nearly singular integrals are converted into bounded integrands without explicit computation of high-order derivatives. The proposed approach is kernel- and dimension-independent, showing accuracy, flexibility, efficiency, and compatibility with fast solvers through large-scale three-dimensional numerical examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
Andreas Karageorghis, Amir Noorizadegan, C. S. Chen
Summary: A Kansa-radial basis function collocation method is proposed for solving high order BVPs in multiply connected domains, where N distinct sets of boundary centers are selected. The efficacy of the proposed approach has been demonstrated through applications in 2D and 3D high order BVPs in multiply connected domains.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics
Sagrario Lantaron, Susana Merchan
Summary: In this study, we examined the Schrodinger operator with a potential q on a disk and the corresponding Dirichlet-to-Neumann (DtN) map. Numerical and analytical results were provided on the map's range and stability for a specific class of one-step radial potentials.
Article
Mathematics
Haiyun Deng, Hairong Liu, Xiaoping Yang
Summary: In this paper, the critical points and critical zero points of solutions to a kind of linear elliptic equations with nonhomogeneous Dirichlet boundary conditions in a multiply connected domain are studied. The geometric structures of interior critical point sets and interior critical zero point sets are obtained based on the analysis of the distributions of connected components of certain level sets. Some theorems regarding the structural properties are presented as well.
ISRAEL JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Helia Serrano, Ramon F. Alvarez-Estrada, Gabriel F. Calvo
Summary: A variety of cell migration processes across tissue boundaries can be modeled using mean first-passage time (MFPT) in confined domains. This study investigates the MFPT functions T on three-dimensional domains Ω, which satisfy a Poisson-like equation and different boundary conditions on the surface S enclosing Ω. By employing potential theory methods, the calculation of T reduces to solving inhomogeneous linear integral equations with singular kernels on S. The integral equation approach allows for analyzing the MFPT with mixed boundary conditions on a closed spherical surface.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
R. U. M. I. N. G. Zhang
Summary: In this paper, a new spectral decomposition method is proposed for simulating wave propagation in complex waveguides. The efficient approximation of the Dirichlet-to-Neumann (DtN) map is crucial for solving waveguide scattering problems numerically. By decomposing the physical solution into a family of generalized eigenfunctions, the DtN map can be explicitly written using these functions. The DtN map is approximated using a finite truncation based on the exponential decay of the generalized eigenfunctions, and the approximation is proven to converge exponentially. The truncated DtN map is utilized to truncate the unbounded domain into a bounded one, and a variational formulation is set up for solving the problem in this bounded domain. The truncated problem is then solved using a finite element method. Error estimation is provided for the numerical algorithm, and numerical examples are provided to demonstrate the efficiency of the algorithm.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2023)
Article
Engineering, Electrical & Electronic
Johan Helsing, Anders Karlsson
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES
(2015)
Article
Computer Science, Interdisciplinary Applications
Johan Helsing, Anders Karlsson
JOURNAL OF COMPUTATIONAL PHYSICS
(2016)
Article
Engineering, Electrical & Electronic
Johan Helsing, Anders Karlsson
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES
(2017)
Article
Mathematics, Applied
Johan Helsing, Karl-Mikael Perfekt
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
(2018)
Article
Mathematics, Applied
Johan Helsing
ABSTRACT AND APPLIED ANALYSIS
(2013)
Article
Mathematics, Applied
Johan Helsing, Anders Holst
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2015)
Article
Mathematics, Applied
Johan Helsing, Karl-Mikael Perfekt
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2013)
Article
Engineering, Electrical & Electronic
Johan Helsing, Anders Karlsson
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2013)
Article
Engineering, Multidisciplinary
Johan Helsing, B. Tomas Johansson
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
(2011)
Article
Computer Science, Interdisciplinary Applications
Johan Helsing
JOURNAL OF COMPUTATIONAL PHYSICS
(2011)
Article
Computer Science, Interdisciplinary Applications
Johan Helsing, Anders Karlsson
JOURNAL OF COMPUTATIONAL PHYSICS
(2014)
Article
Mathematics, Applied
Victor D. Didenko, Johan Helsing
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2013)
Article
Mathematics, Applied
Johan Helsing, Hyeonbae Kang, Mikyoung Lim
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
(2017)
Proceedings Paper
Engineering, Electrical & Electronic
Johan Helsing, Anders Karlsson
PROCEEDINGS OF 2013 URSI INTERNATIONAL SYMPOSIUM ON ELECTROMAGNETIC THEORY (EMTS)
(2013)
Proceedings Paper
Engineering, Electrical & Electronic
R. C. McPhedran, J. Helsing, G. W. Milton
2012 IEEE ANTENNAS AND PROPAGATION SOCIETY INTERNATIONAL SYMPOSIUM (APSURSI)
(2012)
Article
Computer Science, Interdisciplinary Applications
Tian Liang, Lin Fu
Summary: In this work, a new shock-capturing framework is proposed based on a new candidate stencil arrangement and the combination of infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme achieves high order accuracy and resolves genuine discontinuities with sub-cell resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lukas Lundgren, Murtazo Nazarov
Summary: In this paper, a high-order accurate finite element method for incompressible variable density flow is introduced. The method addresses the issues of saddle point system and stability problem through Schur complement preconditioning and artificial compressibility approaches, and it is validated to have high-order accuracy for smooth problems and accurately resolve discontinuities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Gabriele Ciaramella, Laurence Halpern, Luca Mechelli
Summary: This paper presents a novel convergence analysis of the optimized Schwarz waveform relaxation method for solving optimal control problems governed by periodic parabolic PDEs. The analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition, which enables a precise characterization of the convergence factor at the semidiscrete level. The behavior of the optimal transmission condition parameter is also analyzed in detail as the time discretization approaches zero.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jonas A. Actor, Xiaozhe Hu, Andy Huang, Scott A. Roberts, Nathaniel Trask
Summary: This article introduces a scientific machine learning framework that uses a partition of unity architecture to model physics through control volume analysis. The framework can extract reduced models from full field data while preserving the physics. It is applicable to manifolds in arbitrary dimension and has been demonstrated effective in specific problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Summary: This paper proposes a novel strategy called B-spline based SFEM to fundamentally solve the problems of the conventional SFEM. It uses different basis functions and cubic B-spline basis functions with C-2-continuity to improve the accuracy of numerical integration and avoid matrix singularity. Numerical results show that the proposed method is superior to conventional methods in terms of accuracy and convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Timothy R. Law, Philip T. Barton
Summary: This paper presents a practical cell-centred volume-of-fluid method for simulating compressible solid-fluid problems within a pure Eulerian setting. The method incorporates a mixed-cell update to maintain sharp interfaces, and can be easily extended to include other coupled physics. Various challenging test problems are used to validate the method, and its robustness and application in a multi-physics context are demonstrated.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Summary: This paper presents the development of a third-order compact gas-kinetic scheme for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme demonstrates robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Summary: This paper presents a novel Bayesian statistical framework for the characterization of natural subsurface formations, and introduces the concept of multiscale sampling to localize the search in the stochastic space. The results show that the proposed framework performs well in solving inverse problems related to porous media flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jacob Rains, Yi Wang, Alec House, Andrew L. Kaminsky, Nathan A. Tison, Vamshi M. Korivi
Summary: This paper presents a novel method called constrained optimized DMD with Control (cOptDMDc), which extends the optimized DMD method to systems with exogenous inputs and can enforce the stability of the resulting reduced order model (ROM). The proposed method optimally places eigenvalues within the stable region, thus mitigating spurious eigenvalue issues. Comparative studies show that cOptDMDc achieves high accuracy and robustness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Junhong Yue, Peijun Li
Summary: This paper proposes two numerical methods (IP-FEM and BP-FEM) to study the flexural wave scattering problem of an arbitrary-shaped cavity on an infinite thin plate. These methods successfully decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary, providing an effective solution to this challenging problem.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
William Anderson, Mohammad Farazmand
Summary: We develop fast and scalable methods, called RONS, for computing reduced-order nonlinear solutions. These methods have been proven to be highly effective in tackling challenging problems, but become computationally prohibitive as the number of parameters grows. To address this issue, three separate methods are proposed and their efficacy is demonstrated through examples. The application of RONS to neural networks is also discussed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Marco Caliari, Fabio Cassini
Summary: In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Sebastiano Boscarino, Seung Yeon Cho, Giovanni Russo
Summary: This work proposes a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. The method combines a semi-Lagrangian scheme for the convection term, a fast spectral method for computation of the collision operator, and a high order conservative reconstruction and a weighted optimization technique to preserve conservative quantities. Numerical tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jialei Li, Xiaodong Liu, Qingxiang Shi
Summary: This study shows that the number, centers, scattering strengths, inner and outer diameters of spherical shell-structured sources can be uniquely determined from the far field patterns. A numerical scheme is proposed for reconstructing the spherical shell-structured sources, which includes a migration series method for locating the centers and an iterative method for computing the inner and outer diameters without computing derivatives.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)