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In this paper, we present a meshless hybrid method combining the Generalized Finite Difference (GFD) and Finite Difference based Radial Basis Function (RBF-FD) approaches to solve non-homogeneous partial differential equations (PDEs)…
This paper developed a systematic strategy establishing RBF on the wavelet analysis, which includes continuous and discrete RBF orthonormal wavelet transforms respectively in terms of singular fundamental solutions and nonsingular general…
A boundary thickening-based direct forcing (BTDF) immersed boundary (IB) method is proposed for fully resolved simulation of incompressible viscous flows laden with finite size particles. By slightly thickening the boundary thickness, the…
The shifted boundary method (SBM) is an approximate domain method for boundary value problems, in the broader class of unfitted/embedded/immersed methods. It has proven to be quite efficient in handling problems with complex geometries,…
A mechanical model and numerical method for structural membranes implied by all isosurfaces of a level-set function in a three-dimensional bulk domain are proposed. The mechanical model covers large displacements in the context of the…
Machine learning representations of many-body quantum states have recently been introduced as an ansatz to describe the ground states and unitary evolutions of many-body quantum systems. We explore one of the most important representations,…
Restricted Boltzmann Machine (RBM) is an importan- t generative model modeling vectorial data. While applying an RBM in practice to images, the data have to be vec- torized. This results in high-dimensional data and valu- able spatial…
We propose time-domain boundary integral and coupled boundary integral and variational formulations for acoustic scattering by linearly elastic obstacles. Well posedness along with stability and error bounds with explicit time dependence…
Random feature mapping (RFM) is a popular method for speeding up kernel methods at the cost of losing a little accuracy. We study kernel ridge regression with random feature mapping (RFM-KRR) and establish novel out-of-sample error upper…
The concept of trimming, embedding, or immersing geometries into a computational background mesh has gained considerable attention in recent years, particularly in isogeometric analysis (IGA). In this approach, the physical domain is…
A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac…
In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…
We propose a new discretization method for PDEs on moving domains in the setting of unfitted finite element methods, which is provably higher-order accurate in space and time. In the considered setting, the physical domain that evolves…
Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks…
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite…
The Boundary Element Method (BEM) is implemented using piecewise linear elements to solve the two-dimensional Dirichlet problem for Laplace's equation posed on a disk. A benefit of the BEM as opposed to many other numerical solution…
We propose a novel class of temporal high-order parametric finite element methods for solving a wide range of geometric flows of curves and surfaces. By incorporating the backward differentiation formulae (BDF) for time discretization into…
The boundary element method (BEM) enables solving three-dimensional electromagnetic problems using a two-dimensional surface mesh, making it appealing for applications ranging from electrical interconnect analysis to the design of…
The Reduced Basis Method (RBM) is a rigorous model reduction approach for solving parametrized partial differential equations. It identifies a low-dimensional subspace for approximation of the parametric solution manifold that is embedded…
This paper treats the inverse problem of retrieving the electrical conductivity of a material starting from boundary measurements in the framework of Electrical Resistance Tomography (ERT). In particular, the focus is on non-iterative…