IPDAE: Improved Patch-Based Deep Autoencoder for Lossy Point Cloud Geometry Compression

Point cloud is a crucial representation of 3D contents, which has been widely used in many areas such as virtual reality, mixed reality, autonomous driving, etc. With the boost of the number of points in the data, how to efficiently compress point cloud becomes a challenging problem. In this paper, we propose a set of significant improvements to patch-based point cloud compression, i.e., a learnable context model for entropy coding, octree coding for sampling centroid points, and an integrated compression and training process. In addition, we propose an adversarial network to improve the uniformity of points during reconstruction. Our experiments show that the improved patch-based autoencoder outperforms the state-of-the-art in terms of rate-distortion performance, on both sparse and large-scale point clouds. More importantly, our method can maintain a short compression time while ensuring the reconstruction quality.Comment: 12 page

Adaptive Multi-Rate Wavelet Method for Circuit Simulation

In this paper a new adaptive algorithm for multi-rate circuit simulation encountered in the design of RF circuits based on spline wavelets is presented. The ordinary circuit differential equations are first rewritten by a system of (multi-rate) partial differential equations (MPDEs) in order to decouple the different time scales. Second, a semi-discretization by Rothe's method of the MPDEs results in a system of differential algebraic equations DAEs with periodic boundary conditions. These boundary value problems are solved by a Galerkin discretization using spline functions. An adaptive spline grid is generated, using spline wavelets for non-uniform grids. Moreover the instantaneous frequency is chosen adaptively to guarantee a smooth envelope resulting in large time steps and therefore high run time efficiency. Numerical tests on circuits exhibiting multi-rate behavior including mixers and PLL conclude the paper

Differential-Algebraic Equations

Differential-Algebraic Equations (DAE) are today an independent field of research, which is gaining in importance and becoming of increasing interest for applications and mathematics itself. This workshop has drawn the balance after about 25 years investigations of DAEs and the research aims of the future were intensively discussed

Solution of the nonlinear PDAEs by variational iteration method and its applications in nanoelectronics

In this paper, the system of nonlinear partial differential-algebraic equations is solved by the wellknown variational iteration method and the results with high accuracy are obtained by only one iteration. Furthermore, some nanoelectronics models are expressed by partial differential-algebraic equations and one of them is successfully solved by the proposed method. Although solving nonlinear PDAEs is difficult but it is shown that the variational iteration method using Taylor expansion is an efficient method to solve these nonlinear problems

Existence and uniqueness of solution for multidimensional parabolic PDAEs arising in semiconductor modeling

This paper concerns with a compact network model combined with distributed models for semiconductor devices. For linear RLC networks containing distributed semiconductor devices, we construct a mathematical model that joins the differential-algebraic initial value problem for the electric circuit with multi-dimensional parabolic-elliptic boundary value problems for the devices. We prove an existence and uniqueness result, and the asymptotic behavior of this mixed initial boundary value problem of partial differential-algebraic equations

Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.Comment: Preprint of Book Chapte

Existence and uniqueness of solution for multidimensional parabolic PDAEs arising in semiconductor modeling

This paper concerns with a compact network model combined with distributed models for semiconductor devices. For linear RLC networks containing distributed semiconductor devices, we construct a mathematical model that joins the differential-algebraic initial value problem for the electric circuit with multi-dimensional parabolic-elliptic boundary value problems for the devices. We prove an existence and uniqueness result, and the asymptotic behavior of this mixed initial boundary value problem of partial differential-algebraic equations

A multiscale systems approach to microelectronic processes

Abstract This paper describes applications of molecular simulation to microelectronics processes and the subsequent development of techniques for multiscale simulation and multiscale systems engineering. The progression of the applications of simulation in the semiconductor industry from macroscopic to molecular to multiscale is reviewed. Multiscale systems are presented as an approach that incorporates molecular and multiscale simulation to design processes that control events at the molecular scale while simultaneously optimizing all length scales from the molecular to the macroscopic. It is discussed how design and control problems in microelectronics and nanotechnology, including the targeted design of processes and products at the molecular scale, can be addressed using the multiscale systems tools. This provides a framework for addressing the "grand challenge" of nanotechnology: how to move nanoscale science and technology from art to an engineering discipline