This contribution is concerned with the development, analysis and implementation of Adaptive Finite Element Methods (AFEMs) for distributed and boundary control problems with control constraints. AFEMs consist of successive loops of the cycle ’SOLVE’, ’ESTIMATE’, ’MARK’, and ’REFINE’. Emphasis will be on the steps ’SOLVE’ and ’ESTIMATE’. In this context, ’SOLVE’ stands for the efficient solutio...

We provide an adaptive strategy for solving shallow water equations with dynamic grid adaptation including a sparse representation of the bottom topography. A challenge in computing approximate solutions to the shallow water equations including wetting and drying is to achieve the positivity of the water height and the well-balancing of the approximate solution. A key property of our adaptive s...

This paper puts forth a novel algorithm, termed truncated generalized gradient flow (TGGF), to solve for x ∈ R/C a system of m quadratic equations yi = |〈ai,x〉|, i = 1, 2, . . . ,m, which even for {ai ∈ R/C}i=1 random is known to be NP-hard in general. We prove that as soon as the number of equations m is on the order of the number of unknowns n, TGGF recovers the solution exactly (up to a glob...

In our 2008 ISSC paper we have reviewed some pragmatic challenges of incremental system safety assessment and outlined requirements for a framework to identify, track and manage design and analysis changes introduced between iterations. This ‘follow-up’ paper reports our recent work to address these issues. The paper defines an intuitive “lightweight refinement” relation between results of the ...

The differentiating characteristics of text versus images and their impact on large medical image databases intended to allow content-based indexing and retrieval have recently been explored. For the design of powerful user interfaces, we propose a grouping of the various mechanisms into four classes: (i) output modules, (ii) parameter modules, (iii) transaction modules, and (iv) process module...

Motivated by the fact that important real-life problems, such as the protein docking problem, can be accurately modeled by minimizing a nonconvex piecewise-quadratic function, a nonconvex underestimator is constructed as the minimum of a finite number of strictly convex quadratic functions. The nonconvex underestimator is generated by minimizing a linear function on a reverse convex region and ...

A reasonable approach to formal modelling is to start with a specification that captures the requirements of a system and then use formal refinement to implement it. The problem with this approach is that for complex systems the specification itself is complex. It becomes a challenge to say whether the specification is the right one for the given requirements. Sometimes requirements also concer...

We present an algorithm called Tar (“Thread-modular Abstraction Refinement”) for model checking safety properties of concurrent software. The Tar algorithm uses thread-modular assume-guarantee reasoning to overcome the exponential complexity in the control state of multithreaded programs. Thread modularity means that Tar explores the state space of one thread at a time, making assumptions about...

Block matching motion estimation was one of the most important modules in the design of any video encoder. It consumed more than 85% of video encoding time due to searching of a candidate block in the search window of the reference frame. To minimize the search time on block matching, a simplified and efficient Block Matching Algorithm for Fast Motion Estimation was proposed. It had two steps s...

Refinable functions are functions that are in a sense self-similar: If you add shrunken translates of a refinable function in a weighted way, then you obtain that refinable function again. For instance, see Figure 1 for how a quadratic B-spline can be decomposed into four small B-splines and how the so called Daubechies-2 generator function is decomposed into four small variants of itself. All ...