11 papers
High Performance Computing of SDRE models with Discrete Kalman Filtering for Robust -Controls
Yunfeng Cai, Tiexiang Li, Wen-Wei Lin +1
State-dependent Riccati equation (SDRE) control requires repeated online solution of continuous-time algebraic Riccati equations (CAREs). A projected-channel formulation…
Null-Space-Free 6D Spectral Embedding with Local Rayleigh Quotient Recovery for 3D Quasiperiodic Maxwell's Eigenproblems
Teng-Chao Sun, Tiexiang Li, Wen-Wei Lin +1
We develop a numerical framework for three-dimensional quasiperiodic Maxwell eigenvalue problems obtained through a six-dimensional periodic embedding. A projected Bloch--Fourier d…
A Novel Bijective Angle and Volume-preservation Balanced Parameterization for -dimensional Manifolds
Tiexiang Li, Wen-Wei Lin, Zhong-Heng Tan +3
We propose a unified framework for bijective parameterizations of -dimensional manifolds that jointly control angular and volumetric distortion through a weighted combination of…
An Efficient Parity-Blocked Method for Band-Structure Computation of 3D Anisotropic Phononic Crystals
Jingkai Zhang, Xing-Long Lyu, Tiexiang Li +1
Band-structure calculations for three-dimensional anisotropic phononic crystals require the repeated solution of large elastic generalized eigenvalue problems along Bloch paths. In…
A Unified DeepONet Framework for Logarithmically Stable Infinite-Dimensional Inverse Problems
Wen-Jie Wu, Tiexiang Li, Wen-Wei Lin
We develop a unified DeepONet framework for logarithmically stable inverse problems between infinite-dimensional function spaces, with inverse acoustic scattering as a model applic…
A Novel Computational and Analytical Framework for 2D Quasiperiodic Helmholtz Eigenvalue Problems via the Projection Method
Teng-Chao Sun, Tiexiang Li, Wen-Wei Lin +1
In this paper, we propose a spectral framework that embeds 1D and 2D quasiperiodic Helmholtz eigenvalue problems into higher-dimensional (2D and 4D) periodic spaces via the project…
A Unifying Framework for Doubling Algorithms
Changli Liu, Tiexiang Li, Jungong Xue +2
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the al…
A Novel Double Periodic Conformal Flattening Algorithm for Genus-One Surfaces
Zhong-Heng Tan, Tiexiang Li, Wen-Wei Lin +1
In this paper, we propose novel parameterization methods for genus-one surfaces, called the Double Periodic Conformal Flattening (DPCF) algorithm. The desired conformal map is obta…
-Dimensional Volumetric Stretch Energy Minimization for Volume-/Mass-Preserving Parameterizations
Zhong-Heng Tan, Tiexiang Li, Wen-Wei Lin +1
In this paper, we develop an dimensional volumetric stretch energy (-VSE) functional for the volume-/mass-preserving parameterization of the -manifolds topologically equi…
A Robust Hessian-based Trust Region Algorithm for Spherical Conformal Parameterizations
Zhong-Heng Tan, Tiexiang Li, Wen-Wei Lin +1
Surface parameterizations are widely applied in computer graphics, medical imaging and transformation optics. In this paper, we rigorously derive the gradient vector and Hessian ma…
Eigenvalue Problems of Discrete Curl Operators on Various Lattices for Simulating Three Dimensional Photonic Crystals
Huang Tsung-Ming, Li Tiexiang, Li Wei-De +3
There are many numerical methods for simulate three-dimensional photonic crystals, after comparison, we choose Yee's scheme to be our discrete method. So far, this method can only…