Related papers: A hybrid finite volume -- spectral element method …
A nonlinear Helmholtz (NLH) equation with high frequencies and corner singularities is discretized by the linear finite element method (FEM). After deriving some wave-number-explicit stability estimates and the singularity decomposition for…
In this paper we propose and analyze a virtual element method to approximate the natural frequencies of the acoustic eigenvalue problem with polygonal meshes that allow the presence of small edges. With the aid of a suitable seminorm that…
In this paper, we compute the band structure of one- and two-dimensional phononic composites using the extended finite element method (X-FEM) on structured higher-order (spectral) finite element meshes. On using partition-of-unity…
This work is concerned with a unique combination of high order local absorbing boundary conditions (ABC) with a general curvilinear Finite Element Method (FEM) and its implementation in Isogeometric Analysis (IGA) for time-harmonic acoustic…
We present a multiscale mixed finite element method for solving second order elliptic equations with general $L^{\infty}$-coefficients arising from flow in highly heterogeneous porous media. Our approach is based on a multiscale spectral…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
We present the Finite Element Method (FEM) for the numerical solution of the multidimensional coefficient inverse problem (MCIP) in two dimensions. This method is used for explicit reconstruction of the coefficient in the hyperbolic…
In this paper, a recently proposed approach to multizone sound field synthesis, referred to as Joint Pressure and Velocity Matching (JPVM), is investigated analytically using a spherical harmonics representation of the sound field. The…
The Landau-Lifshitz equation describes the dynamics of magnetization in ferromagnetic materials. Due to the essential nonlinearity and nonconvex constraint, it is typically solved numerically. In this paper, we developed a finite volume…
We present a novel fully implicit hybrid finite volume/finite element method for incompressible flows. Following previous works on semi-implicit hybrid FV/FE schemes, the incompressible Navier-Stokes equations are split into a pressure and…
The scattering and transmission of harmonic acoustic waves at a penetrable material are commonly modelled by a set of Helmholtz equations. This system of partial differential equations can be rewritten into boundary integral equations…
Flow instabilities, wave propagation phenomena, and structural interaction are current topics of the field "Flow acoustics" also named "Aeroacoustics". Assuming the theory of classical mechanics, aeroacoustic applications are modeled by the…
Acoustic velocity vectors (AVVs) are related to the human's perception of sound at low frequencies and are widely used in Ambisonics. This paper proposes a spatial sound field reproduction algorithm called velocity matching, which…
Audio super-resolution is challenging owing to its ill-posed nature. Recently, the application of diffusion models in audio super-resolution has shown promising results in alleviating this challenge. However, diffusion-based models have…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…
In this paper, a semi-discrete spatial finite volume (FV) method is proposed and analyzed for approximating solutions of anomalous subdiffusion equations involving a temporal fractional derivative of order $\alpha \in (0,1)$ in a…
The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming…
We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) motivated by \cite{MR3980476,GL18} to solve the singularly perturbed convection-diffusion equations. The main idea is to first establish a…
The continuum description of active particle systems is an efficient instrument to analyze a finite size particle dynamics in the limit of a large number of particles. However, it is often the case that such equations appear as nonlinear…