Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.

Analysis on the off-state design and characterization of LIGBTs in partial SOI technology

Classical high voltage devices fabricated on SOI substrates suffer from a backside coupling effect which could result in premature breakdown. This phenomenon becomes more prominent if the structure is an IGBT which features a p-type injector. To suppress the premature breakdown due to crowding of electro-potential lines within a confined SOI/buried oxide structure, the partial SOI (PSOI) technique is being introduced. This paper analyzes the off-state behavior of an n-type Superjunction (SJ) LIGBT fabricated on PSOI substrate. During the initial development stage the SJ LIGBT was found to have very high leakage. This was attributed to the back and side coupling effects. This paper discusses these effects and shows how this problem could be successfully addressed with minimal modifications of device layout. The off-state performance of the SJ LIGBT at different temperatures is assessed and a comparison to an equivalent LDMOSFET is given. © 2014 Elsevier Ltd. All rights reserved.

Fixed-rank matrix factorizations and Riemannian low-rank optimization

Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the geometric framework of optimization on Riemannian quotient manifolds. We study the underlying geometries of several well-known fixed-rank matrix factorizations and then exploit the Riemannian quotient geometry of the search space in the design of a class of gradient descent and trust-region algorithms. The proposed algorithms generalize our previous results on fixed-rank symmetric positive semidefinite matrices, apply to a broad range of applications, scale to high-dimensional problems, and confer a geometric basis to recent contributions on the learning of fixed-rank non-symmetric matrices. We make connections with existing algorithms in the context of low-rank matrix completion and discuss the usefulness of the proposed framework. Numerical experiments suggest that the proposed algorithms compete with state-of-the-art algorithms and that manifold optimization offers an effective and versatile framework for the design of machine learning algorithms that learn a fixed-rank matrix. © 2013 Springer-Verlag Berlin Heidelberg.