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  • Solving moving-boundary problems with multiquadric function, level set method and adaptive greedy algorithm
    Vrankar, Leopold ; Turk, Goran ; Runovc, Franc
    Moving-boundary problems are often called Stefan problems, with the reference to the early work of J. Stefan, around 1890, when he was interested in the melting of the polar ice cap. Within this ... frame a large number of important physical processes involving heat conduction and materials undergoing a change of phase can be included. One of these processes is a heat transfer problem involving a phase change due to solidification or melting. That is important in many industrial applications such as the drilling of high ice-content soil, the storage of thermal energy, the safety studies of nuclear reactors and fire studies. Moving boundaries are also associated with time-dependent problems and the position of the boundary has to be determined as a function of time and space, but it depends also on basic variables of the problems. Various numerical methods are known to solve Stefan problems, e.g. front-tracking, front-fixing, and fixed-domain methods. The finite-difference methods and finite-element techniques have been used extensively for numerical solution of moving boundary problems. Recent research on the numerical method has focused on the idea of using a meshless methodology for the numerical solution of partial differential equations (PDEs). One of the common characteristics of all mesh-free methods is their ability to construct functional approximation or interpolation entirely from the information at a set of scattered nodes, among which there is no relationship. During the past decade, increasing attention has been given to the development of meshless methods using radial basis functions (e.g. multiquadric -MQ) for the numerical solution of PDEs. The usual method of solving PDEs with radial basis functions (RBFs) is similar to standard mesh based methods by constructing a uniform grid that is consecutively refined, yielding progressively to more ill-conditioned systems of equations. Many efforts have been made to find a new computational method that is capable of overcoming the ill-conditioning problems using linear solvers. A level set method has become an attractive design tool for tracking, modelling and simulating the motion of free boundaries in fluid mechanics, combustion, computer animation and image processing. The goal is to include MQ RBFs into level set method to construct a more efficient approach and stabilize the solution process with the adaptive greedy algorithm.
    Vir: Conference proceedings [Elektronski vir] (Str. 909.1-909.8)
    Vrsta gradiva - prispevek na konferenci
    Leto - 2009
    Jezik - angleški
    COBISS.SI-ID - 560880

vir: Proceedings [Elektronski vir] (Str. 909.1-909.8)

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