# Poster Presentations

Midwest Numerical Analysis Day

## Poster Presentation

**Vasileios Kalantzis**, University of Minnesota*Beyond AMLS: Domain Decomposition with Rational Filtering*

This poster discusses the software package Cucheb, a GPU implementation of the filtered Lanczos procedure for the solution of large sparse symmetric eigenvalue problems. The filtered Lanczos procedure uses a carefully chosen polynomial spectral transformation to accelerate convergence of the Lanczos method when computing eigenvalues within a desired interval. This method has proven particularly effective for eigenvalue problems that arise in electronic structure calculations and density functional theory. We compare our implementation against an equivalent CPU implementation and show that using the GPU can reduce the computation time by more than a factor of 10.

**Avary Kolasinski**, University of Kansas*A Surface Moving Mesh Method Based on Equidistribution and Alignment*

We will discuss a surface moving mesh method that is based on the equidistribution and alignment conditions. Then we will formulate a meshing functional for this surface mesh method. Finally, we will present numerical results in both 2-D and 3-D.

**Agnieszka Miedlar**, University of Kansas Flexible *Krylov Subspace Interior Eigensolvers*

Determining excited states in quantum physics or calculating the number of valence electrons in the Density Functional Theory (DFT) involve solving eigenvalue problems of very large dimensions. Moreover, very often the interesting features of these complex systems go beyond information contained in the extreme eigenpairs. For this reason, it is important to consider iterative solvers developed to compute a large amount of eigenpairs in the middle of the spectrum of large Hermitian and non-Hermitian matrices. In this talk, we present newly developed Krylov-type methods and compare them with the well-established techniques in electronic structure calculations. We demonstrate their efficiency and robustness through various numerical examples. This is a joint work with Yousef Saad (University of Minnesota).

**Truong Nguyen**, Wright State University*Domain Decomposition for Computing Adaptive Moving Mesh Using Parabolic Monge- Ampere Equation*

We propose an iterative or parallel method to compute the adaptive moving mesh by solving the Parabolic Monge-Ampere (PMA) equation. In particular, the physical domain is partitioned into sub-domain in slab or block-decomposition. PMA equation is solved independently for the steady state solution on each sub domain. The adaptive grid is then computed via the gradient of the steady state solution of PMA equation. Finally, the method uses the classical Schwarz's iteration to update the boundary points of the adaptive mesh.

**Xiaofeng Ou**, Purdue University*Matrix Aspect of Fast Multipole Method*

The fast multipole method has a strong physics background, so it is hard for non-physics people to understand its essence. This talk aims to reveal the essence of 2D-FMM in matrix language. Also its connection with the hierarchical semiseparable matrices(HSS) will be explored. We can show that FMM matrix admits a HSS representation. Hence we can perform common operations in linear complexity, such as the matrix vector product and ULV factorization.

**Chunjae Park**, Konkuk University*New Error Analysis of Scott-Vogelius Finite Elements*

We will analyse the error on implementing Scott-Vogelius finite elements to solve Stokes equations over singular meshes.

**Hong Zhang**, Utrecht University*Numerical Investigation of Two-Phase Flow with Dynamic Capillary Pressure Moving Mesh Refinement*

Numerical modeling of two-phase flow incorporating dynamic capillary pressure is investigated. The effects of the dynamic coefficient, the infiltrating flux rate and the initial and boundary values are systematically studied using a traveling wave ansatz and efficient numerical methods. The traveling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver. Comparisons between the computed solutions using the Brooks-Corey model and the laboratory measurements of saturation overshoot verify the effectiveness of our approach.