Adjoint DSMC for nonlinear Boltzmann equation constrained optimization

Adjoint Lattice Boltzmann Equation for Parameter Identification

The Lattice Boltzmann Equation is briefly introduced using moments to clearly separate the propagation and collision steps in the dynamics. In order to identify unknown parameters we introduce a cost function and adapt control theory to the Lattice Boltzmann Equation to get expressions for the derivatives of the cost function vs. parameters. This leads to an equivalent of the adjoint method wit...

Towards Adjoint Based Constrained Optimization

Adjoint Lattice Boltzmann for Topology Optimization on multi-GPU architecture

In this paper we present a topology optimization technique applicable to a broad range of flow design problems. We propose also a discrete adjoint formulation effective for a wide class of Lattice Boltzmann Methods (LBM). This adjoint formulation is used to calculate sensitivity of the LBM solution to several type of parameters, both global and local. The numerical scheme for solving the adjoin...

Adjoint method for a tumor growth PDE-constrained optimization problem

In this paper we present a method for estimating unknown parameters that appear on an avascular, spheric tumour growth model. The model for the tumour is based on nutrient driven growth of a continuum of live cells, whose birth and death generate volume changes described by a velocity field. The model consists on a coupled system of partial differential equations whose spatial domain is the tum...

Nonlinear Interactive Multiobjective Optimization Method for Radiotherapy Treatment Planning with Boltzmann Transport Equation