Huidong Yang

Ulrich Langer, Huidong Yang

In this paper, we consider a monolithic approach to handle coupled fluid-structure interaction problems with different hyperelastic models in an all-at-once manner. We apply Newton's method in the outer iteration dealing with nonlinearities of the coupled system. We discuss preconditioned Krylov sub-space, algebraic multigrid and algebraic multilevel methods for solving the linearized algebraic equations. Finally, we compare the results of the monolithic approach with those of the corresponding partitioned approach that we studied in our previous work.

Ulrich Langer, Huidong Yang

This paper deals with balanced domain decomposition by constraints (BDDC) method for solving large-scale linear systems of algebraic equations arising from the space-time finite element discretization of parabolic initial-boundary value problems. The time is considered as just another spatial coordinate, and the finite elements are continuous and piecewise linear on unstructured simplicial space-time meshes. We consider BDDC preconditioned GMRES methods for solving the space-time finite element Schur complement equations on the interface. Numerical studies demonstrate robustness of the preconditioners to some extent.

Huidong Yang

In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of equations arising from the finite element discretization of the vector Laplacian problem, linear elasticity problem in pure displacement and mixed displacement-pressure form, and Stokes problem in mixed velocity-pressure form in 3D, respectively. We use hierarchical quadratic basis functions to construct the finite element spaces. A new heuristic algebraic coarsening strategy is introduced for construction of the hierarchical coarse system matrices. We focus on numerical study of the mesh-independence robustness of the algebraic multigrid and the algebraic multigrid preconditioned Krylov subspace methods.

Cankun Qiu, Zhi Luo, Xia Wu et al.

The light scattering of multilayer nanoparticles can be solved by Maxwell equations. However, it is difficult to solve the inverse design of multilayer nanoparticles by using the traditional trial-and-error method. Here, we present a method for forward simulation and inverse design of multilayer nanoparticles. We combine the global search ability of genetic algorithm with the local search ability of neural network. First, the genetic algorithm is used to find a suitable solution, and then the neural network is used to fine-tune it. Due to the non-unique relationship between physical structures and optical responses, we first train a forward neural network, and then it is applied to the inverse design of multilayer nanoparticles. Not only here, this method can easily be extended to predict and find the best design parameters for other optical structures.

Yican Chen, Zhi Luo, Xia Wu et al.

Fourier ptychography is a recently explored imaging method for overcoming the diffraction limit of conventional cameras with applications in microscopy and yielding high-resolution images. In order to splice together low-resolution images taken under different illumination angles of coherent light source, an iterative phase retrieval algorithm is adopted. However, the reconstruction procedure is slow and needs a good many of overlap in the Fourier domain for the continuous recorded low-resolution images and is also worse under system aberrations such as noise or random update sequence. In this paper, we propose a new retrieval algorithm that is based on convolutional neural networks. Once well trained, our model can perform high-quality reconstruction rapidly by using the graphics processing unit. The experiments demonstrate that our model achieves better reconstruction results and is more robust under system aberrations.

Ulrich Langer, Huidong Yang

In this work, we develop a cutting method for solving problems with moving and growing interfaces in 3D. This new method is able to resolve large displacement or deformation of immersed objects by combining the Arbitrary Lagrangian-Eulerian method with only small local mesh deformation defined on the reference domain, that is decomposed into the macro-elements. The linear system of algebraic equations arising after the temporal and spatial discretizations of a model parabolic interface heat-conduction-like problem with vector-valued functions is solved by either an all-at-once or a segregated algebraic multigrid method.