We discuss the design of parallel algorithms to solve elliptic problems on multi-clusters computers. Multi-clusters can be seen as two-level parallel architecture machines, since communication between clusters are usually much slower than communication or access to memory within each of the clusters. We introduce special algorithms that use two levels of parallelism and match the multi-cluster ...

In this paper we give a new decomposition algorithm that breaks a multilevel relation into single-level relations and a new recovery algorithmwhich reconstructs the original multilevel relation from the decomposed single-level relations. There are several novel aspects to our decomposition and recovery algorithms which provide substantial advantages over previous proposals: (1) Our algorithms a...

Image restoration has drawn much attention in recent years and a surge of research has been done on variational models and their numerical studies. However, there remains an urgent need to develop fast and robust methods for solving the minimization problems and the underlying nonlinear PDEs to process images of moderate to large size. This paper aims to propose a two-level domain decomposition...

Discrete wavelet transform (DWT) has been widely adopted in biomedical signal processing for denoising, compression and so on. Choosing a suitable decomposition level (DL) in DWT is of paramount importance to its performance. In this paper, we propose to exploit sparseness of the transformed signals to determine the appropriate DL. Simulation results have shown that the sparseness of transforme...

In this paper, we consider multilevel relations in which security classi cations are assigned at the granularity of individual data elements. Usually these multilevel relations exist only at the logical level. In reality, a multilevel relation is decomposed into a collection of single level base relations which are then physically stored in a database, and a recovery algorithm is used to recons...

In this paper, we propose a new heuristic to find common subexpressions of given Boolean functions based on Shannon-type factoring. This heuristic limits the search space of finding common subexpressions considerably by applying a top-down approach. In this top-down approach, synthesis of a Boolean network flows from the primary outputs to the primary inputs. The common subexpressions and their...

n this paper, we consider a two-level problem of resource allocation in a telecommunication network divided into zones. At the upper level the network manager distributes homogeneous resource shares among zones in order to maximize the total network profit, which takes into account the inner zonal payments from users and the implementation costs. This means that each zonal income calculation at...

Recent advances of high performance computing systems permits extreme scale computational simulation with high resolution numerical models. For uncertainty quantification of such extreme scale simulations, the computational cost of the traditional Monte Carlo simulations (MCS) may become extremely high. As an efficient alternative to MCS, the intrusive spectral stochastic finite element method ...

We focus on the robust principal component analysis (RPCA) problem, and review a range of old and new convex formulations for the problem and its variants. We then review dual smoothing and level set techniques in convex optimization, present several novel theoretical results, and apply the techniques on the RPCA problem. In the final sections, we show a range of numerical experiments for simul...

This paper presents a time-efficient method for the decomposition and resynthesis of speed-independent (SI) circuits. Given the specification of an SI circuit, our method first generates its standard C implementation. Then, the combinational decomposition is performed to decompose each high-fanin gate that does not exist in the gate library into some available low-fanin gates. The time efficien...