May 24, 2019   7:08 p.m. Ela
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Semi-implicit methods for solution of partial differential equations

Supervisor: doc. RNDr. Peter Frolkovič, PhD.


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Project description:Novel time discretization methods for numerical solution of partial differential equations of hyperbolic and parabolic type will be developed. Numerical schemes will be unconditionally stable for arbitrary choice of time steps without introducing time splitting errors. The important properties of exact solution like conservation laws and maximum principle will be preserved in discrete form that will enable physically correct numerical solutions in real applications. High-resolution form of methods will be derived, i.e. high-order accurate when solution is smooth with a local reduction of accuracy for other parts. Specialized solvers for resulting systems of algebraic equations will be implemented. In summary the obtained methods will be used with locally refined computational grids without CFL restriction and large time steps will be possible when stationary solutions are approached. This advantages will be exploited in level set methods with grid adaptivity near interfaces and artificial time relaxations.
Kind of project:VEGA ()
Department:Department of Mathematics and Constructive Geometry (FCE)
Project identification:1/0728/15
Project status:In process of execution
Project start date :01. 01. 2015
Project close date:31. 12. 2018
Number of workers in the project:2
Number of official workers in the project:0