Related papers: Multiscale-Spectral GFEM and Optimal Oversampling
We introduce quantitative and robust tools to control the numerical accuracy in simulations performed using the Multiscale Finite Element Method (MsFEM). First, we propose a guaranteed and fully computable a posteriori error estimate for…
In this paper, a local-global model reduction method is presented to solve stochastic optimal control problems governed by partial differential equations (PDEs). If the optimal control problems involve uncertainty, we need to use a few…
Traditional simulation of complex mechanical systems relies on numerical solvers of Partial Differential Equations (PDEs), e.g., using the Finite Element Method (FEM). The FEM solvers frequently suffer from intensive computation cost and…
In this paper, we propose a Bayesian approach for multiscale problems with the availability of dynamic observational data. Our method selects important degrees of freedom probabilistically in a Generalized multiscale finite element method…
Pan-sharpening algorithms utilize a panchromatic image and a multispectral image to generate a high spatial and high spectral image. However, the optimizations of the algorithms are designed with different standards. We employ a simple…
Meshfree methods, including the reproducing kernel particle method (RKPM), have been widely used within the computational mechanics community to model physical phenomena in materials undergoing large deformations or extreme topology…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…
In this paper we develop a class of efficient Galerkin boundary element methods for the solution of two-dimensional exterior single-scattering problems. Our approach is based upon construction of Galerkin approximation spaces confined to…
Beam prediction is an effective approach to reduce training overhead in massive multiple-input multiple-output (MIMO) systems. However, existing beam prediction models still exhibit limited generalization ability in diverse scenarios, which…
In many applications, the training data for a machine learning task is partitioned across multiple nodes, and aggregating this data may be infeasible due to communication, privacy, or storage constraints. Existing distributed optimization…
This study presents a generalized multiscale multimesh finite element method ($\text{M}^2$-FEM) that addresses several long-standing challenges in the numerical simulation of integral structural theories, often used to model multiscale and…
The Multiscale Finite Element Method (MsFEM) is developed in the vein of Crouzeix-Raviart element for solving viscous incompressible flows in genuine heterogeneous media. Such flows are relevant in many branches of engineering, often at…
In this paper we propose an enhanced version of the residual sub-sampling method (RSM) in [9] for adaptive interpolation by radial basis functions (RBFs). More precisely, we introduce in the context of sub-sampling methods a maximum profile…
We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known…
In this work, a multiple-expert binarization framework for multispectral images is proposed. The framework is based on a constrained subspace selection limited to the spectral bands combined with state-of-the-art gray-level binarization…
Finite element method (FEM) is one of the most important numerical methods in modern engineering design and analysis. Since traditional serial FEM is difficult to solve large FE problems efficiently and accurately, high-performance parallel…
This paper introduces an innovative end-to-end model-based deep learning approach for efficient electromagnetic analysis of high-dimensional frequency selective surfaces (FSS). Unlike traditional data-driven methods that require large…
General Sparse Matrix-Matrix Multiplication (SpGEMM) has attracted much attention from researchers in graph analyzing, scientific computing, and deep learning. Many optimization techniques have been developed for different applications and…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
The Generalized Finite Element Method (GFEM) is an effective unfitted numerical method for handling interface problems. By augmenting the standard FEM space with an appropriate enrichment space, GFEM can accurately capture C^0 solutions…