## The Factorization Method for Inverse Problems

*Andreas Kirsch and Natalia Grinberg*

- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199213535
- eISBN:
- 9780191707629
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213535.001.0001
- Subject:
- Mathematics, Applied Mathematics

This book is devoted to problems of shape identification in the context of (inverse) scattering problems and problems of impedance tomography. In contrast to traditional methods which are based on ... More

## Boundaries and Geometries

*Gary A. Glatzmaier*

### in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0010
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter examines how boundary and geometry affect convection. It begins with a discussion of how one can implement “absorbing” top and bottom boundaries, which reduce the large-amplitude ... More

## The factorization method for other types of inverse obstacle scattering problems

*Andreas Kirsch and Natalia Grinberg*

### in The Factorization Method for Inverse Problems

- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199213535
- eISBN:
- 9780191707629
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213535.003.0002
- Subject:
- Mathematics, Applied Mathematics

This chapter studies some examples of inverse scattering problems in which the data operator fails to be normal. The impedance boundary condition, the reconstruction from limited-angle data, and the ... More

## Nonconforming finite element methods

*Klaus Böhmer*

### in Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199577040
- eISBN:
- 9780191595172
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577040.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Nonconforming FEMs avoid the strong restrictions of conforming FEMs. So discontinuous ansatz and test functions, approximate test integrals, and strong forms are admitted. This allows the proof of ... More

## Algorithmic Development

*Peter Monk*

### in Finite Element Methods for Maxwell's Equations

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198508885
- eISBN:
- 9780191708633
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508885.003.0013
- Subject:
- Mathematics, Numerical Analysis

This chapter examines the phase error problem and also shows, via a dispersion analysis, that higher order methods can significantly improve phase accuracy. Once a solution is computed it is ... More

## The mixed boundary value problem

*Andreas Kirsch and Natalia Grinberg*

### in The Factorization Method for Inverse Problems

- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199213535
- eISBN:
- 9780191707629
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213535.003.0003
- Subject:
- Mathematics, Applied Mathematics

For the mixed boundary value problem, the scattering domain D consists of several components with different types of boundary conditions. The chapter begins by reviewing results on uniqueness and ... More

## HYPERBOLIC REDUCTIONS OF THE FIELD DQUATIONS

*Miguel Alcubierre*

### in Introduction to 3+1 Numerical Relativity

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199205677
- eISBN:
- 9780191709371
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199205677.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

From the early 1990s, a large number of alternative formulations of the 3+1 evolution equations have been proposed. There are currently more formulations than there are numerical groups capable of ... More

## Equation-Free Computation: An Overview of Patch Dynamics

*G. Samaey, A. J. Roberts, and I. G. Kevrekidis*

### in Multiscale Methods: Bridging the Scales in Science and Engineering

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.003.0008
- Subject:
- Mathematics, Applied Mathematics

This chapter overviews recent progress in the development of patch dynamics, an essential ingredient of the equation-free framework. In many applications we have a given detailed microscopic ... More

## THE HOMOGENEOUS IBVP

*Sylvie Benzoni-Gavage and Denis Serre*

### in Multi-dimensional hyperbolic partial differential equations: First-order systems and applications

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199211234
- eISBN:
- 9780191705700
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211234.003.0007
- Subject:
- Mathematics, Applied Mathematics

When the boundary condition is homogeneous, one may think that there is no data at the boundary and that there is no need of boundary estimates in the maximal estimates. This is reminiscent of the ... More

## Nonlinear Finite-Amplitude Dynamics

*Gary A. Glatzmaier*

### in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0004
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter modifies the numerical code by adding the nonlinear terms to produce finite-amplitude simulations. The nonlinear terms are calculated using a Galerkin method in spectral space. After ... More

## BOUNDARY CONDITIONS FOR EULER EQUATIONS

*Sylvie Benzoni-Gavage and Denis Serre*

### in Multi-dimensional hyperbolic partial differential equations: First-order systems and applications

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199211234
- eISBN:
- 9780191705700
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211234.003.0014
- Subject:
- Mathematics, Applied Mathematics

The nature of an IBVP for a gas depends on the sign of the normal velocity, and on the sub- and super-sonicity. This chapter proceeds to a classification, describing which boundary conditions are ... More

## THE NEUMANN PROBLEM AND PROBLEMS ON MANIFOLDS

*Juan Luis Vázquez*

### in The Porous Medium Equation: Mathematical Theory

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198569039
- eISBN:
- 9780191717468
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198569039.003.0011
- Subject:
- Mathematics, Mathematical Physics

This chapter completes the investigation of previous chapters on the Dirichlet and Cauchy problems by applying the techniques to other important problems. It selects two directions, the Neumann ... More

## FRIEDRICHS-SYMMETRIC DISSIPATIVE IBVPs

*Sylvie Benzoni-Gavage and Denis Serre*

### in Multi-dimensional hyperbolic partial differential equations: First-order systems and applications

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199211234
- eISBN:
- 9780191705700
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211234.003.0003
- Subject:
- Mathematics, Applied Mathematics

This chapter provides an elementary introduction to Initial Boundary Value Problems (IBVP). It introduces the notion of dissipative boundary condition, here in a classical sense. Such IBVPs can be ... More

## Variational Theory for the Cavity Problem

*Peter Monk*

### in Finite Element Methods for Maxwell's Equations

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198508885
- eISBN:
- 9780191708633
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508885.003.0004
- Subject:
- Mathematics, Numerical Analysis

This chapter presents a standard variational method based on the electric field for the cavity problem to prepare for the finite element approximation of this problem. Mixed boundary conditions ... More

## Alternative sampling and probe methods

*Andreas Kirsch and Natalia Grinberg*

### in The Factorization Method for Inverse Problems

- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199213535
- eISBN:
- 9780191707629
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213535.003.0007
- Subject:
- Mathematics, Applied Mathematics

The Factorization Method is not the only sampling method. This final chapter introduces three alternative methods which belong to this class but, in contrast to the Factorization Method, are based on ... More

## NUMERICAL METHODS

*Miguel Alcubierre*

### in Introduction to 3+1 Numerical Relativity

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199205677
- eISBN:
- 9780191709371
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199205677.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

There are many ways to solve partial differential equations numerically. The most popular methods are: finite differencing, finite elements, and spectral methods. This chapter describes the main ... More

## Discontinuous Galerkin methods (DCGMs), with V. Dolejší

*Klaus Böhmer*

### in Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199577040
- eISBN:
- 9780191595172
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577040.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 7 presents with V. Dolejší presents discontinuous Galerkin methods (DCGMs): violated boundary conditions and continuity of the piecewise polynomials are compensated by additional penalty ... More

## Parameterization and implementation issues

*Bijan Mohammadi and Olivier Pironneau*

### in Applied Shape Optimization for Fluids

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199546909
- eISBN:
- 9780191720482
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546909.003.0006
- Subject:
- Mathematics, Mathematical Physics

This chapter presents parameterization and geometrical issues. This is also one of key points for an efficient OSD platform. It describes different strategies for shape deformation within and without ... More

## Field Quantization and Vacuum Energy in the Presence of Boundaries

*M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko*

### in Advances in the Casimir Effect

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199238743
- eISBN:
- 9780191716461
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199238743.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

From the standpoint of quantum field theory, the Casimir effect is related to the vacuum polarization that arises in quantization volumes restricted by boundaries or in spaces with nontrivial ... More

## The Casimir Effect For Two Ideal-Metal Planes

*M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko*

### in Advances in the Casimir Effect

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199238743
- eISBN:
- 9780191716461
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199238743.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter considers the simple but most important configuration of two parallel ideal-metal planes. First, the theory of the scalar and electromagnetic Casimir effects between parallel planes is ... More