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Certifying Solutions for Numerical Constraints

Related publications (52)

Singular quadratic eigenvalue problems: linearization and weak condition numbers

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

SPRINGER2023

Maximum Radiation Efficiency of an Implantable Antenna: The Role of High-Order Modes

Anja Skrivervik, Mingxiang Gao, Jakub Liska

A combination of two numerical techniques of computational electromagnetics, namely, method of moments and vector spherical wave expansion, is used to show performance limitations on the radiation efficiency of implantable antennas and to efficiently resol ...

IEEE2023

Fast in vivo assay of creatine kinase activity in the human brain by P-31 magnetic resonance fingerprinting

Lijing Xin, Daniel Wenz, Mark Stephan Widmaier, Songi Lim

A new and efficient magnetisation transfer P-31 magnetic resonance fingerprinting (MT-P-31-MRF) approach is introduced to measure the creatine kinase metabolic rate kCK

{k}_{\mathrm{CK}}

between phosphocreatine (PCr) and adenosine triphosphate (ATP) i ...

WILEY2023

TimeEvolver: A program for time evolution with improved error bound

Sebastian Zell

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

ELSEVIER2022

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

Giacomo Garegnani

In this thesis we explore uncertainty quantification of forward and inverse problems involving differential equations. Differential equations are widely employed for modeling natural and social phenomena, with applications in engineering, chemistry, meteor ...

EPFL2021

Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

Dimitrios Gourzoulidis

This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...

EPFL2021

Efficient algorithms for wave problems

Boris Bonev

Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others.Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineeri ...

EPFL2021

MATHICSE Technical Report : A probabilistic finite element method based on random meshes: Error estimators and Bayesian inverse problems

Assyr Abdulle, Giacomo Garegnani

We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows to introduce a pr ...

EPFL2021

Novel corrector problems with exponential decay of the resonance error for numerical homogenization

Edoardo Paganoni

Multiscale problems, such as modelling flows through porous media or predicting the mechanical properties of composite materials, are of great interest in many scientific areas. Analytical models describing these phenomena are rarely available, and one mus ...

EPFL2020

Penalization and Bayesian numerical methods for multiscale inverse problems

Andrea Di Blasio

In this thesis we consider inverse problems involving multiscale elliptic partial differential equations. The name multiscale indicates that these models are characterized by the presence of parameters which vary on different spatial scales (macroscopic, m ...

EPFL2019

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Fast in vivo assay of creatine kinase activity in the human brain by P-31 magnetic resonance fingerprinting

Lijing Xin, Daniel Wenz, Mark Stephan Widmaier, Songi Lim

A new and efficient magnetisation transfer P-31 magnetic resonance fingerprinting (MT-P-31-MRF) approach is introduced to measure the creatine kinase metabolic rate kCK

{k}_{\mathrm{CK}}

between phosphocreatine (PCr) and adenosine triphosphate (ATP) i ...

WILEY2023