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We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…

Numerical Analysis · Mathematics 2024-10-04 Ngoc Cuong Nguyen

The paper describes a numerical method for solving acoustic multibody scattering problems in two and three dimensions. The idea is to compute a highly accurate approximation to the scattering operator for each body through a local…

Numerical Analysis · Mathematics 2026-03-20 Yunhui Cai , Joar Bagge , Per-Gunnar Martinsson

A $p$-adaptive discontinuous Galerkin time-domain method is developed to obtain high-order solutions to electromagnetic scattering problems. A novel feature of the proposed method is the use of divergence error to drive the $p$-adaptive…

Computational Physics · Physics 2022-11-15 Apurva Tiwari , Avijit Chatterjee

We present a higher-order extension of the dual cell method for the time-domain Maxwell equations in three spatial dimensions. The approach builds upon a variational reinterpretation of the Finite Integration Technique on dual meshes and…

Numerical Analysis · Mathematics 2026-04-16 Lorenzo Codecasa , Bernard Kapidani , Joachim Schöberl , Markus Wess

To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional…

Numerical Analysis · Mathematics 2026-01-19 Jiyu Liu , Zhixuan Li , Jiatu Yan , Zhiqi Li , Qinghai Zhang

This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This…

Numerical Analysis · Mathematics 2018-09-26 Ali Özcan , Stefan Kollmannsberger , John N. Jomo , Ernst Rank

This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…

Numerical Analysis · Mathematics 2017-08-10 Binjie Li , Hao Luo , Xiaoping Xie

Integral-equation-based fast direct solvers for electromagnetic scattering can substantially reduce computational costs, especially in the presence of multiple excitations. We recently proposed a new high-frequency fast direct solver…

Numerical Analysis · Mathematics 2026-03-05 V. Giunzioni , C. Henry , A. Merlini , F. P. Andriulli

We present an efficient dimension-by-dimension finite-volume method which solves the adiabatic magnetohydrodynamics equations at high discretization order, using the constrained-transport approach on Cartesian grids. Results are presented…

Numerical Analysis · Mathematics 2024-07-29 Jean-Mathieu Teissier , Wolf-Christian Müller

We investigate the properties of some recently developed variable-order differential operators involving order transition functions of exponential type. Since the characterisation of such operators is performed in the Laplace domain it is…

Numerical Analysis · Mathematics 2023-09-19 Roberto Garrappa , Andrea Giusti

The generalized-$\alpha$ time-marching method provides second-order accuracy in time and controls the numerical dissipation in the high-frequency region of the discrete spectrum. This method includes a wide range of time integrators. We…

Numerical Analysis · Mathematics 2019-06-17 Pouria Behnoudfar , Quanling Deng , Victor M. Calo

In this paper, we study numerical methods for the solution of partial differential equations on evolving surfaces. The evolving hypersurface in $\Bbb{R}^d$ defines a $d$-dimensional space-time manifold in the space-time continuum…

Numerical Analysis · Mathematics 2014-04-09 Maxim A. Olshanskii , Arnold Reusken , Xianmin Xu

In this paper we study propagation of the high frequency electromagnetic waves in a curved spacetime. We discuss a so call spinoptics approach which generalizes a well known geometric optics approximation and allows one to take into account…

General Relativity and Quantum Cosmology · Physics 2024-08-26 Valeri P. Frolov

We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…

Numerical Analysis · Mathematics 2022-06-29 Xianyi Zeng , Giovanni Stabile , Efthymios N. Karatzas , Guglielmo Scovazzi , Gianluigi Rozza

An in-domain finite dimensional controller for a class of distributed parameter systems on a one-dimensional spatial domain formulated under the port-Hamiltonian framework is presented. Based on [25] where positive feedback and a late…

Optimization and Control · Mathematics 2023-02-06 Ning Liu , Yongxin Wu , Yann Le Gorrec , Laurent Lefevre , Hector Ramirez

This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing…

Numerical Analysis · Mathematics 2026-02-10 Yuming Ba , Liang Chen , Yaru Chen , Qiuqi Li

In this paper, exact solutions to the problem of acoustic scattering by elastic spherical symmetric scatterers are developed. The scatterer may consist of an arbitrary number of fluid and solid layers, and scattering with single Neumann…

Mathematical Physics · Physics 2022-04-21 Jon Vegard Venås , Trond Jenserud

In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…

Optimization and Control · Mathematics 2025-09-04 Huynh Khanh , Bui Trong Kien

We propose a new class of high-order time-marching schemes with dissipation user-control and unconditional stability for parabolic equations. High-order time integrators can deliver the optimal performance of highly-accurate and robust…

Numerical Analysis · Mathematics 2021-02-12 Pouria Behnoudfar , Quanling Deng , Victor M. Calo

First-order energy dissipative schemes in time are available in literature for the Poisson-Nernst-Planck (PNP) equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite…

Numerical Analysis · Mathematics 2023-09-08 Jie Ding , Shenggao Zhou