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Annalisa Buffa | |
---|---|

Buffa at Oberwolfach in 2007 | |

Born | 1973 (age 45–46) |

Nationality | Italian |

Alma mater | University of Milan |

Occupation | Mathematician |

**Annalisa Buffa** (14 February 1973) is an Italian mathematician, specializing in numerical analysis and PDEs.

**Numerical analysis** is the study of algorithms that use numerical approximation for the problems of mathematical analysis. Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life sciences, social sciences, medicine, business and even the arts have adopted elements of scientific computations. The growth in computing power has revolutionized the use of realistic mathematical models in science and engineering, and subtle numerical analysis is required to implement these detailed models of the world. For example, ordinary differential equations appear in celestial mechanics ; numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.

In mathematics, a **partial differential equation** (**PDE**) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a computer model. A special case is ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.

Buffa received her master's degree in computer engineering in 1996 and in 2000 her Ph.D., with supervisor Franco Brezzi, from the University of Milan with thesis *Some numerical and theoretical problems in computational electromagnetism*.^{ [1] } She was from 2001 to 2004 a Researcher, from 2004 to 2013 a Research Director (rank equivalent to Professor), and from 2013 to 2016 she was the Director at the Istituto di matematica applicata e tecnologie informatiche "E. Magenes" (IMATI) of the CNR in Pavia. From 2016 to present she is Professor of Mathematics and holds the Chair of Numerical Modeling and Simulation at EPFL.

**Franco Brezzi** is an Italian mathematician.

The **University of Milan**, or **University of Studies of Milan**, known colloquially as *UniMi* or *Statale*, is a higher education institution in Milan, Italy. It is one of the largest universities in Europe, with about 60,000 students, and a permanent teaching and research staff of about 2,000.

**Pavia** is a town and comune of south-western Lombardy in northern Italy, 35 kilometres south of Milan on the lower Ticino river near its confluence with the Po. It has a population of c. 73,000. The city was the capital of the Kingdom of the Lombards from 572 to 774.

She has been a visiting scholar at many institutions, including the *Laboratoire Jacques-Louis Lions* at the University of Paris VI, the École Polytechnique, the ETH Zürich, and the University of Texas at Austin (Institute for Computational Engineering and Sciences, ICES).

**École Polytechnique** is a French public institution of higher education and research in Palaiseau, a suburb located south from Paris. It is one of the leading prestigious French Grandes écoles in engineering, especially known for its *polytechnicien* engineering program.

**The University of Texas at Austin** is a public research university in Austin, Texas. It was founded in 1883 and is the flagship institution of the University of Texas System. The University of Texas was inducted into the Association of American Universities in 1929, becoming only the third university in the American South to be elected. The institution has the nation's eighth-largest single-campus enrollment, with over 50,000 undergraduate and graduate students and over 24,000 faculty and staff.

Buffa's research deals with a wide range of topics in PDEs and numerical analysis: "isogeometric analysis, fully compatible discretization of PDEs, linear and non linear elasticity, contact mechanics, integral equations on non-smooth manifolds, functional theory for Maxwell equations in non-smooth domains, finite element techniques for Maxwell equations, non-conforming domain decomposition methods, asymptotic analysis, stabilization techniques for finite element discretizations."^{ [2] }

Buffa was awarded in 2007 the Bartolozzi Prize and in 2015 the Collatz Prize "for her spectacular use of deep and sophisticated mathematical concepts to obtain outstanding contributions to the development of computer simulations in science and industry" (Laudatio).^{ [3] } In 2014 she was an Invited Speaker at the International Congress of Mathematicians in Seoul with talk *Spline differential forms*. In 2008 she received an ERC Starting Grant and in 2016 an ERC Advanced Grant.

The **Bartolozzi Prize** is awarded by the Italian Mathematical Union every two years. Until 2017 it has been awarded to an Italian mathematician below the age of 34. Starting with the 2019 edition the prize has been reserved to female Italian mathematicians below the age of 40. The prize is entitled in the memory of the Italian mathematician Giuseppe Bartolozzi and is worth €3,000.

The **International Congress of Mathematicians** (**ICM**) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).

**Seoul**, officially the **Seoul Special City**, is the capital and largest metropolis of South Korea. With surrounding Incheon metropolis and Gyeonggi province, Seoul forms the heart of the Seoul Capital Area.

**Computational fluid dynamics** (**CFD**) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests.

**Feng Kang** was a Chinese mathematician and scientist. He was elected an academician of the Chinese Academy of Sciences in 1980. After his death, the Chinese Academy of Sciences established the Feng Kang Prize in 1994 to reward young Chinese researchers who made outstanding contributions to computational mathematics.

**Numerical partial differential equations** is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs).

The **boundary element method** (**BEM**) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations. including fluid mechanics, acoustics, electromagnetics, fracture mechanics, and contact mechanics.

**Stanley Osher** is an American mathematician, known for his many contributions in shock capturing, level-set methods, and PDE-based methods in computer vision and image processing. Osher is a professor at the University of California, Los Angeles (UCLA), Director of Special Projects in the Institute for Pure and Applied Mathematics (IPAM) and member of the California NanoSystems Institute (CNSI) at UCLA. He has a daughter, Kathryn, and a son, Joel.

**Mesh generation** is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells. Often these cells form a simplicial complex. Usually the cells partition the geometric input domain. Mesh cells are used as discrete local approximations of the larger domain. Meshes are created by computer algorithms, often with human guidance through a GUI, depending on the complexity of the domain and the type of mesh desired. The goal is to create a mesh that accurately captures the input domain geometry, with high-quality (well-shaped) cells, and without so many cells as to make subsequent calculations intractable. The mesh should also be fine in areas that are important for the subsequent calculations.

**Computational electromagnetics** (**CEM**), **computational electrodynamics** or **electromagnetic modeling** is the process of modeling the interaction of electromagnetic fields with physical objects and the environment.

**Computational mechanics** is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science as a "third way" besides theoretical and experimental sciences, computational mechanics was widely considered to be a sub-discipline of applied mechanics. It is now considered to be a sub-discipline within computational science.

In the field of numerical analysis, **meshfree methods** are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Meshfree methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort. The absence of a mesh allows Lagrangian simulations, in which the nodes can move according to the velocity field.

The **J. H. Wilkinson Prize for Numerical Software** is awarded every four years to honor outstanding contributions in the field of numerical software. The award is named to commemorate the outstanding contributions of James H. Wilkinson in the same field.

The **International Council for Industrial and Applied Mathematics (ICIAM)** is a worldwide organisation for professional applied mathematics societies, and for other societies with a significant interest in industrial or applied mathematics. The current (2016) President is Maria J. Esteban and the Executive Secretary is Sven Leyffer.

**Philippe G. Ciarlet** is a French mathematician, known particularly for his work on mathematical analysis of the finite element method. He has contributed also to elasticity, to the theory of plates ans shells and differential geometry.

The **finite element method** (**FEM**) is a numerical method for solving problems of engineering and mathematical physics. Typical problem areas of interest include structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The analytical solution of these problems generally require the solution to boundary value problems for partial differential equations. The finite element method formulation of the problem results in a system of algebraic equations. The method approximates the unknown function over the domain. To solve the problem, it subdivides a large system into smaller, simpler parts that are called finite elements. The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.

**Jinchao Xu** is an American-Chinese mathematician. He is currently the Verne M. Willaman Professor in the Department of Mathematics at the Pennsylvania State University, University Park. He is known for his work on multigrid methods, domain decomposition methods, finite element methods, and more recently deep neural networks.

**Thomas Yizhao Hou** is the Charles Lee Powell Professor of Applied and Computational Mathematics in the Department of Computing and Mathematical Sciences at the California Institute of Technology. He is known for his work in numerical analysis and mathematical analysis.

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