An ALE ESFEM for solving PDEs on evolving surfaces [PDF]
, 2012 Numerical methods for approximating the solution of partial differential equations on evolving hypersurfaces using surface finite elements on evolving triangulated surfaces are presented.
Vanessa Styles (4460662) +3 more
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Mesh-Free RBF-FD Method with Polyharmonic Splines and Polynomials for High-Dimensional PDEs and Financial Option Pricing [PDF]
Control and Optimization in Applied MathematicsThis study employs the radial basis function-generated finite difference (RBF-FD) method to address high-dimensional elliptic differential equations under Dirichlet boundary conditions.
Narges Hosseinzadeh +2 more
doaj +1 more source
A system of degenerate parabolic nonlinear PDE's: a new free boundary problem
Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications, 2005 We prove existence of solutions of a new free boundary problem described by a system of degenerate parabolic equations. The problem arises in petroleum engineering and concerns fluid flows in diatomite rocks. The unknown functions represent the pressure of the fluid and a damage parameter of the porous rock.
M. Bertsch, R. Dal Passo, NITSCH, CARLO
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Optimal Control of Singular Parabolic PDEs Modeling Multiphase Stefan-type Free Boundary Problems
, 2020 Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control problems is introduced via finite differences.
Abdulla, Ugur G., Cosgrove, Evan
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Accelerated pseudo-transient method for elastic, viscoelastic, and coupled hydromechanical problems with applications [PDF]
Geoscientific Model DevelopmentThe accelerated pseudo-transient (APT) method is a matrix-free approach used to solve partial differential equations (PDEs), characterized by its reliance on local operations, which makes it highly suitable for parallelization.
Y. Alkhimenkov, Y. Y. Podladchikov
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Poisson Structures for PDEs Associated with Diffeomorphism Groups [PDF]
, 2004 We study Poisson and Lie-Poisson structures on the diffeomorphism groups with a smooth metric spray in connection with dynamics of nonlinear PDEs. In particular, we provide a precise analytic sense in which the time t map for the Euler equations of an ...
Vasylkevych, Sergiy
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On numerical simulation of liquid polymer moulding
Mathematical Modelling and Analysis, 2003 In this paper we consider numerical algorithms for solving the system of nonlinear PDEs, arising in modeling of liquid polymer injection. We investigate the particular case when a porous preform is located within the mould, so that the liquid polymer is ...
R. Čiegis, O. Iliev
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Walk on Stars: A Grid-Free Monte Carlo Method for PDEs with Neumann Boundary Conditions
, 2023 Grid-free Monte Carlo methods based on the walk on spheres (WoS) algorithm solve fundamental partial differential equations (PDEs) like the Poisson equation without discretizing the problem domain or approximating functions in a finite basis.
Gkioulekas, Ioannis +3 more
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On quantum and relativistic mechanical analogues in mean field spin models [PDF]
, 2014 Conceptual analogies among statistical mechanics and classical or quantum mechanics often appeared in the literature. For classical two-body mean field models, such an analogy is based on the identification between the free energy of Curie-Weiss type ...
Guerra, F. +10 more
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A mesh-free method for interface problems using the deep learning approach
, 2020 In this paper, we propose a mesh-free method to solve interface problems using the deep learning approach. Two types of PDEs are considered. The first one is an elliptic PDE with a discontinuous and high-contrast coefficient.
WANG, Z, Zhang, Z
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