Melting interfaces in induction heated bodies

PDEs in connection with optics and electromagnetic theory (35Q60) Stefan problems, phase changes, etc. (80A22) Magnetohydrodynamics and electrohydrodynamics (76W05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Applications to the sciences (65Z05)

Cites Work

The inverse electromagnetic shaping problem
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A new method for inverse electromagnetic casting problems based on the topological derivative
On the numerical integration of a parabolic differential equation subject to a moving boundary condition
Modelling dendritic solidification with melt convection using the extended finite element method
A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids
A vertex-based hierarchical slope limiter for \(p\)-adaptive discontinuous Galerkin methods
Étude de la déformation d'un liquide magnétique (Study of the deformation of a magnetic liquid)
Finite Hankel transforms of distributions
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The fast construction of extension velocities in level set methods
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Stefan problem through extended finite elements: review and further investigations
A moving mesh method for the solution of the one-dimensional phase-field equations
Level set methods and dynamic implicit surfaces
Implementation of an X-FEM solver for the classical two-phase Stefan problem
Solution of the equilibrium problem in electromagnetic casting considering a solid inclusion in the melt
A finite element based level set method for two-phase incompressible flows
Numerical modelling of electromagnetic casting processes
Moving and deforming finite-element simulation of two-dimensional Stefan problems
On time integration in the XFEM
Moving boundary-moving mesh analysis of phase change using finite elements with transfinite mappings
Computing geodesic paths on manifolds
Fluid dynamical aspects of the levitation-melting process
Magnetic levitation of liquid metals
On a two-dimensional magnetohydrodynamic problem. I. Modelling and analysis
NUMERICAL MODELING OF INDUCTION HEATING FOR TWO-DIMENSIONAL GEOMETRIES
The extended finite element method (XFEM) for solidification problems
On a two-dimensional magnetohydrodynamic problem. II. Numerical analysis
Mathematical Models for Eddy Currents and Magnetostatics
On strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method
Heat conduction in a melting solid
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