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A Bermúdez–Moreno algorithm adapted to solve a viscoplastic problem in alloy solidification processes

P. Barral, P. Quintela, M. T. Sánchez (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The aim of this work is to present a computationally efficient algorithm to simulate the deformations suffered by a viscoplastic body in a solidification process. This type of problems involves a nonlinearity due to the considered thermo-elastic-viscoplastic law. In our previous papers, this difficulty has been solved by means of a duality method, known as Bermúdez–Moreno algorithm, involving a multiplier which was computed with a fixed point algorithm or a Newton method. In this paper, we will...

A boundary multivalued integral “equation” approach to the semipermeability problem

Jaroslav Haslinger, Charalambos C. Baniotopoulos, Panagiotis D. Panagiotopoulos (1993)

Applications of Mathematics

The present paper concerns the problem of the flow through a semipermeable membrane of infinite thickness. The semipermeability boundary conditions are first considered to be monotone; these relations are therefore derived by convex superpotentials being in general nondifferentiable and nonfinite, and lead via a suitable application of the saddlepoint technique to the formulation of a multivalued boundary integral equation. The latter is equivalent to a boundary minimization problem with a small...

A brief review of some application driven fast algorithms for elliptic partial differential equations

Prabir Daripa (2012)

Open Mathematics

Some application driven fast algorithms developed by the author and his collaborators for elliptic partial differential equations are briefly reviewed here. Subsequent use of the ideas behind development of these algorithms for further development of other algorithms some of which are currently in progress is briefly mentioned. Serial and parallel implementation of these algorithms and their applications to some pure and applied problems are also briefly reviewed.

A. C. Clarke's Space Odyssey and Newton's law of gravity

Bartoň, Stanislav, Renčín, Lukáš (2017)

Programs and Algorithms of Numerical Mathematics

In his famous tetralogy, Space Odyssey, A. C. Clarke called the calculation of a motion of a mass point in the gravitational field of the massive cuboid a classical problem of gravitational mechanics. This article presents a proposal for a solution to this problem in terms of Newton's theory of gravity. First we discuss and generalize Newton's law of gravitation. We then compare the gravitational field created by the cuboid -- monolith, with the gravitational field of the homogeneous sphere. This...

A C1-P2 finite element without nodal basis

Shangyou Zhang (2008)

ESAIM: Mathematical Modelling and Numerical Analysis


A new finite element, which is continuously differentiable, but only piecewise quadratic polynomials on a type of uniform triangulations, is introduced. We construct a local basis which does not involve nodal values nor derivatives. Different from the traditional finite elements, we have to construct a special, averaging operator which is stable and preserves quadratic polynomials. We show the optimal order of approximation of the finite element in interpolation, and in solving the biharmonic...

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