The Powell–Sabin (PS) piecewise quadratic C finite element on the PS 12-split of a triangulation is a common choice for the construction of a BPX-type preconditioner for the biharmonic equation. In this note we investigate the related Powell–Sabin element on the PS 6-split instead of the PS 12-split for the construction of such preconditioners. For the PS 6-split element multilevel spaces can b...

Design of blast resistant structures is an important subject in structural engineering, attracting the attention of governments, researchers, and engineers. Thus, given the benefits of optimization in engineering, development and assessment of optimization methods for optimum design of structures against blast is of great importance. In this research, multi-objective optimization of steel momen...

We consider the problem of constructing a C1 piecewise quadratic interpolant, Q, to positional and gradient data defined at the vertices of a tessellation of n-simplices in IR. The key to the interpolation scheme is to appropriately subdivide each simplex to ensure that certain necessary geometric constraints are satisfied by the subdivision points. We establish these constraints using the Bern...

A fast algorithm has been developed for solving a class of least squares Problems arising in adaptive Signal processing. The algorithm is based on the Powell and Zangwill direction set method for unconstrained minimization Problems and is designed so as to fully take advantage of the special structure of the adaptive least squares (ALS) problems. It is a fast algorithm because it requires only ...

Solar-terrestrial interactions produce a rich variety of optical emissions in the Earth’s upper atmosphere (100–1000 km). While ground based brightness measurements (i.e., column integrated photon density) provide an important diagnostic of these processes, the more interesting physics is in the associated volume emission rate distribution (i.e., photon production/cm s versus altitude). This wo...

A fast algorithm, called the direction set based algorithm, has been developed recently for solving a class of adaptive least squares problems arising in signal processing. The algorithm is based on the direction set method developed by Powell and Zangwill for solving unconstrained minimization problems without using derivatives. It is designed so as to fully take advantage of the special struc...

In this talk, we study a fast total variation minimization method for image restoration. In the proposed method, we use the exact total variation minimization scheme to denoise the deblurred image. An alternating minimization algorithm is employed to solve the proposed total variation minimization problem. Our experimental results show that the quality of restored images by the proposed method ...