This paper takes a uniform look at the customized applications of proximal point algorithm (PPA) to two classes of problems: the linearly constrained convex minimization problem with a generic or separable objective function and a saddle-point problem. We model these two classes of problems uniformly by a mixed variational inequality, and show how PPA with customized proximal parameters can yie...

This paper considers the inexact Barzilai-Borwein algorithm applied to saddle point problems. To this aim, we study the convergence properties of the inexact Barzilai-Borwein algorithm for symmetric positive definite linear systems. Suppose that gk and g̃k are the exact residual and its approximation of the linear system at the k-th iteration, respectively. We prove the R-linear convergence of t...

The Cedar multi{cluster system is a machine with several levels of par-allelism and memory. We compare two diierent Cedar{implementations of a Navier{ Stokes solver kernel, the Generalized Stokes problem which is discretized here by a Mixed Finite Element Method. The arising linear system is solved by the conjugate gradient Uzawa algorithm. The two implementation approaches are a static approac...

Cell-free circulating nucleic acids in human blood are increasing being researched as a source of diagnostic and prognostic biomarkers for clinical oncology. High copy number per cell and frequent mutations in various malignancies make mitochondrial genome an attractive target for such an investigation, but practical development and validation of biomarkers based on cell-free mitochondrial DNA ...

In this article, we extend our Distributed Lagrange Multiplier/Fictitious Domain method previously implemented on simple regular Cartesian grids to quadtree/octree adaptive grids. The objective is improve both the accuracy and efficiency of DLM/FD particle-resolved simulation by extending its computing capabilities through dynamic local mesh refinement. main features numerical method, such as a...