##### Department of Mathematics,

University of California San Diego

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### Special Colloquium

## Yingda Cheng

#### University of Texas at Austin

## Discontinuous Galerkin Schemes for Boltzmann Equations in Semiconductor Device Simulation

##### Abstract:

\indent In recent years, kinetic transport models have received a lot of attention in various fields, including semiconductor device modeling, plasma physics, etc. This talk will focus on the Boltzmann equation, which is one of the most important equations in statistical physics. The Boltzmann equations describe the time evolution of the probability density functions, and are generally composed of a transport part and a collision part. Those equations have a lot of interesting structures that comes from applications and are computationally challenging to solve. In this talk, we will look into two classes of Boltzmann equations: one being the Boltzmann-Poisson systems in semiconductor device simulations, and the other being the linear Vlasov-Boltzmann transport equations. The goal is to design computationally efficient schemes that can preserve the important structures of the physical systems. I will motivate the choice of the discontinuous Galerkin (DG) finite element methods for treating those equations. The DG schemes enjoy the advantage of conservative formulation, flexibility for arbitrarily unstructured meshes, with a compact stencil, and with the ability to easily accommodate arbitrary h-p adaptivity. Numerical issues such as implementation, algorithm design and analysis for suitable applications will be addressed. Benchmark numerical tests will be provided to demonstrate the performance of the scheme compared to existing solvers such as Monte-Carlo and finite difference solvers.

Host: Li-Tien Cheng

### February 1, 2011

### 2:00 PM

### AP&M 6402

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