Quadrature by Expansion: A New Method for the Evaluation of Layer Potentials

Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior domains. The practical application of these methods, however, requires the accurate evaluation of boundary integrals with singular, weakly singular or nearly singular kernels. Historically, these issues have been handled either by low-order product integration rules (computed semi-analytically), by singularity subtraction/cancellation, by kernel regularization and asymptotic analysis, or by the construction of special purpose "generalized Gaussian quadrature" rules. In this paper, we present a systematic, high-order approach that works for any singularity (including hypersingular kernels), based only on the assumption that the field induced by the integral operator is locally smooth when restricted to either the interior or the exterior. Discontinuities in the field across the boundary are permitted. The scheme, denoted QBX (quadrature by expansion), is easy to implement and compatible with fast hierarchical algorithms such as the fast multipole method. We include accuracy tests for a variety of integral operators in two dimensions on smooth and corner domains

On Protection by Layout Randomization

Layout randomization is a powerful, popular technique for software protection. We present it and study it in programming-language terms. More specifically, we consider layout randomization as part of an implementation for a high-level programming language; the implementation translates this language to a lower-level language in which memory addresses are numbers. We analyze this implementation, by relating low-level attacks against the implementation to contexts in th

A bootstrap method for sum-of-poles approximations

A bootstrap method is presented for finding efficient sum-of-poles approximations of causal functions. The method is based on a recursive application of the nonlinear least squares optimization scheme developed in (Alpert et al. in SIAM J. Numer. Anal. 37:1138–1164, 2000), followed by the balanced truncation method for model reduction in computational control theory as a final optimization step. The method is expected to be useful for a fairly large class of causal functions encountered in engineering and applied physics. The performance of the method and its application to computational physics are illustrated via several numerical examples

QuaC: Binary Optimization for Fast Runtime Code Generation in C

) Curtis Yarvin Adam Sah Abstract Runtime code generation (RTCG) has considerable theoretical potential but has so far seen little use in practice. Adequate tools are lacking. We present QuaC, an RTCG system that lets C programmers specialize their functions at runtime with a simple, portable user interface. QuaC works by applying compiler optimization techniques to machine code in memory. It is fast and highly retargetable. 1 Introduction In theory, runtime code generation is an extremely powerful technique. Code runs faster when specialized to the current data; and often at runtime data stays constant long enough to be worth the investment of specialized code. Routines specialized to runtime constants will be smaller and faster. This is not a new idea, and in the past many systems have explored the field. Before compilers or an emphasis on portability became widespread, most software was written in assembly language, and programmers found it natural and common to use self-modifyi..