Explicit time advancement for continuous finite elements requires the inversion of a global mass matrix. For spectral element simulations on quadrilaterals and hexahedra, there is an accurate approximate matrix which diagonal, making it computationally efficient explicit simulations. In this article shown that standard space polynomials used with triangular elements, denoted $\mathcal{T}(p)$, w...

This paper investigates the inverse problem of determining the unknown time-dependent leading coefficient in the parabolic equation using the usual conditions of the direct problem and an additional condition. An algorithm is developed for solving numerically the inverse problem using the technique of space decomposition in a reproducing kernel space. The leading coefficients can be solved by a...

Recently, Azam, Arshad and Beg [4] introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we introduce the notion of c-chainable cone rectangular metric space and we establish a fixed point theorem for uniformly locally contractive mappings in such spaces. An example is given to illustrate...

We describe a new data format for storing triangular and symmetric matrices called RFP (Rectangular Full Packed). The standard two dimensional arrays of Fortran and C (also known as full format) that are used to store triangular and symmetric matrices waste nearly half the storage space but provide high performance via the use of level 3 BLAS. Standard packed format arrays fully utilize storage...

In this paper we discuss different approaches for exploiting parallelism in the ICCG method for solving large sparse symmetric positive ,lefinite systems of equations on a shared memory parallel computer. Techniques for efficiently solving triangular systems and computing sparse matrix-vector prodm:ts are explored. Three methods for scheduling the tasks in solving triangular systems are impleme...

We devise and study experimentally adaptive strategies driven by a posteriori error estimates to select automatically both the space mesh and the polynomial degree in the numerical approximation of diffusion equations in two space dimensions. The adaptation is based on equilibrated flux estimates. These estimates are presented here for inhomogeneous Dirichlet and Neumann boundary conditions, fo...

Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for t...