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Topic: Dirichlet boundary condition

Related Topics

Neumann boundary condition

Dirichlet function

Dirichlet character

Dirichlet

Dirichlet series

Dirichlet kernel

Dirichlet tessellation

Pigeonhole principle

Salmon Chase

Nathaniel Bowditch

Kerry Wood (baseball player)

Screeching Weasel

Ottawa, Ontario

Alexander Graham Bell

Hyattville, Wyoming

	Dirichlet boundary condition - Wikipedia, the free encyclopedia
		In mathematics, a Dirichlet boundary condition imposed on an ordinary differential equation or a partial differential equation specifies the values a solution is to take on the boundary of the domain.
		Dirichlet boundary conditions are perhaps the easiest to understand but there are many other conditions possible.
		For example, there is the Neumann boundary condition or the mixed boundary condition which is a combination of the Dirichlet and Neumann conditions.
	en.wikipedia.org /wiki/Dirichlet_boundary_condition (161 words)

	Johann Peter Gustav Lejeune Dirichlet - Wikipedia, the free encyclopedia
		Dirichlet was born in Düren, where his father was the postmaster.
		He married Rebecka Mendelssohn Bartholdy, who came from a distinguished family of converts from Judaism to Christianity; she was a granddaughter of the philosopher Moses Mendelssohn, daughter of Abraham Mendelssohn Bartholdy and a sister of the composer Felix Mendelssohn Bartholdy.
		After his death, Dirichlet's lectures and other results in number theory were collected, edited and published by his friend and fellow mathematician Richard Dedekind under the title Vorlesungen über Zahlentheorie (Lectures on Number Theory).
	en.wikipedia.org /wiki/Johann_Peter_Gustav_Lejeune_Dirichlet (312 words)

	Setting the Boundary Conditions
		Boundary conditions are specified as modifiers during the walk of the perimeter of the domain.
		With Laplace's equation, the NATURAL boundary condition is equivalent to the Neumann or normal derivative boundary condition.
		This name associates the boundary condition with one of the listed equations, for it is in reality the equation that is modified by the boundary condition.
	www.pdesolutions.com /userguide/settingtheboundarycondition.htm (306 words)

	QMG project: The finite element package
		Boundary conditions are specified on facets, that is, faces of the brep of dimension d-1 (assuming the dimension of the brep is d).
		Boundary conditions are specified on internal boundaries (both MTL and SL internal boundaries) in the same way as on ordinary boundaries.
		A Neumann condition on an internal boundary is understood as a prespecified jump on cdu/dn as the boundary* crossed.
	www.cs.cornell.edu /Info/People/vavasis/qmg1.0/fe.html (2064 words)

	Mathematica Documentation: Boundary Conditions
		The first method is to differentiate the boundary conditions with respect to the temporal variable and solve for the resulting differential equation(s) at the boundary.
		The Neumann boundary condition was handled using the idea of reflection, which worked fine for a second order finite difference approximation, but does not generalize quite as easily to higher order (though it can be done easily for this problem by computing the entire reflection).
		Technically, it is not necessary that the discretization of the boundary condition be done with the same difference order as the rest of the DE; in fact, since the error terms for the one-sided derivatives are much larger, it may sometimes be desirable to increase the order near the boundaries.
	documents.wolfram.com /mathematica/Built-inFunctions/AdvancedDocumentation/DifferentialEquations/NDSolve/PartialDifferentialEquations/TheNumericalMethodOfLines/BoundaryConditions.html (1488 words)

	Robot Motion Planning
		Boundary Conditions are required for solving the Laplace's equations.
		Since the boundary conditions are fixed, the flow must be along the outward normal of the obstacle surface.
		Neumann boundary conditions causes the robot to graze past the obstacles in their way to the goal (as shown in Results: Problem 1, Neumann boundary conditions).
	members.rediff.com /mitulsaha/rmp.html (1223 words)

	The QMG Finite Element Solver
		Boundary conditions, conductivity and source terms are all associated with the brep rather than the mesh (unlike some other finite element software packages).
		Boundary conditions are specified on facets, that is, faces of the brep of dimension d−1 (assuming the dimension of the brep is d).
		Boundary conditions are specified on internal boundaries (both multiple-region and repeated-boundary internal boundaries) in the same way as on ordinary boundaries.
	www.cs.cornell.edu /info/people/vavasis/qmg2.0/fe.html (1999 words)

	[No title]
		We impose the Dirichlet and Neumann boundary condition on opposite sides of the strip.
		In the present paper we consider curved planar quantum wires, where Dirichlet boundary condition is imposed on one side of the wire, while the Neumann boundary condition is imposed on the opposite side.
		Roughly speaking at least one bound state always exists if the Neumann boundary condition is imposed on the "outer side" of the boundary, \ie\ the one which is locally longer.
	www.ma.utexas.edu /mp_arc/papers/02-189 (1701 words)

	Editing Boundary Conditions: (Site not responding. Last check: 2007-10-13)
		As in the Initial Conditions Patch Editor, one may enter a parsable algebraic expression which is used to calculate boundary condition values over the patch.
		To apply time-varying Dirichlet conditions to a subregion of this or any other existing patch, enter the values and the end time for that value for each entry of the time series into the table (see Figure 15.a).
		The boundary conditions are determined by overwriting patches in space-time using the order in which the patches appear in the patch list.
	www.math.sc.edu /~sharpley/G3D_www/node20.html (352 words)

	SERIES (a Latin word f... - Online Information article about SERIES (a Latin word f...
		Riemann and P. Dirichlet have shown that the terms of a semi-convergent series may be so arranged as to make the series converge to any assigned value or even to diverge.
		The condition of convergency may be otherwise stated; it must be possible to take T so large that the sum Rm,, for all terms um,,.
		Consider the case in which m and n are always positive, and the boundary is the rectangle formed by x=m, y=n, and the axes.
	encyclopedia.jrank.org /SCY_SHA/SERIES_a_Latin_word_from_serere.html (5488 words)

	Stationary Problems in Coefficient Form (Site not responding. Last check: 2007-10-13)
		In finite element terminology, Neumann boundary conditions are also called natural boundary conditions, since they do not occur explicitly in the weak form of the PDE problem.
		Dirichlet conditions are called essential boundary conditions since they restrict the trial space.
		in the Neumann boundary condition is the transpose of h.
	www-math.cudenver.edu /~jmandel/doc/refman/comman14.htm (756 words)

	Overview of PDE Models (Site not responding. Last check: 2007-10-13)
		The second equation is referred to as a generalized Neumann boundary condition, and the third equation is referred to as a Dirichlet boundary condition.
		The generalized Neumann boundary condition is also referred to as a mixed boundary condition, or a Robin boundary condition.
		Together with the Dirichlet condition, this is the weak form of the coefficient form PDE problem.
	www-math.cudenver.edu /~jmandel/doc/guide/guide86.htm (1615 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		The mixed boundary value problems for wave equation are studied in an unbounded domains with smooth non-compact boundaries.
		In particular, conservative problem (Dirichlet boundary condition) in domains with star-shaped boundary are studied in [1].
		The problem with dissipative boundary condition (Dirichlet boundary condition on the star-shaped part of boundary and impedance boundary condition on the non-star-shaped part) are researchded in [2].
	www.zarm.uni-bremen.de /gamm98/num_abs/a151.html (231 words)

	PlanetMath:
		Dirichlet approximation theorem (=Dirichlet's approximation theorem) owned by Koro
		Dirichlet convolution (in arithmetic function) owned by mathcam
		Dirichlet's theorem on primes in arithmetic progressions owned by vitriol
	planetmath.org /encyclopedia/D (1639 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		We compare three different types of boundary conditions representing impenetrable walls of the strip in the sense that there is no probability current through the boundary.
		That is, we again observe the effect of stronger binding of the particle in the case when a Dirichlet boundary curve of the strip is replaced by the Neumann one.
		Assuming that the boundary is sufficiently regular, to impose the Dirichlet boundary conditions means to require the vanishing of wavefunctions, however, as pointed out in~\cite{FTsutsui}, this may be in general too restrictive and one should rather require the vanishing of the probability current only.
	www.ma.utexas.edu /mp_arc/papers/03-264 (5639 words)

	Reference Guide (Site not responding. Last check: 2007-10-13)
		The first equation is satisfied inside the domain, and the second and third equations are both satisfied on the boundary of the domain.
		We refer to the second equation as a generalized Neumann boundary condition, and the third equation as a Dirichlet boundary condition.
		In a structural mechanics model, this term is exactly the reaction force necessary to satisfy the kinematic constraints described by the Dirichlet conditions.
	www.csc.fi /cschelp/sovellukset/math/matlab/femlab/femlab/command14.htm (454 words)

	Dirichlet Boundary Conditions (Site not responding. Last check: 2007-10-13)
		The boundary conditions in any fluid simulation are expressed either in terms of the fluid velocity at the boundary or the velocity gradient at the boundary.
		A method for imposing a Dirichlet boundary condition, for a fixed boundary, to a lattice Boltzmann fluid is devised by Noble et al.
		Here the density, and hence the pressure, at the boundary is calculated by the algorithm to be correct for the desired boundary condition.
	www.ph.ed.ac.uk /~jmb/thesis/node85.html (390 words)

	Development Focus: New Thermal Stress Model for FLOW-3D (Site not responding. Last check: 2007-10-13)
		In its original formulation, the model employed a Dirichlet-type boundary condition (BC) for the solution of the Poisson equation for pressure.
		In Version 9.0, when solving the continuity equation for pressure, two types of boundary conditions can be used at inter-block boundaries: a von Neumann type (where normal velocity is defined) or the Dirichlet type (where pressure is defined).
		When α=0.0, then a pure Dirichlet type boundary condition is used and when α=1.0, then the Neumann type boundary condition is employed.
	www.flow3d.com /newsletters/04/fall04mb.htm (470 words)

	Math 621 - Project Presentations
		When homogeneous Neumann conditions are used the estimates for the finite element solution are similar to the ones obtained for the same problem with Dirichlet boundary conditions.
		In the case of Neumann boundary conditions, in order to prove existence and uniqueness of a weak solution, some assumptions must be made on the domain and its boundary.
		The system is modeled using the homogeneous heat equation with Neumann boundary conditions along the entire outside boundary of the system and a Dirchelet boundary condition describing the constant temperature of the hot water pipe.
	www.math.umbc.edu /~gobbert/teaching/teaching1997to2004/math621.f2003/program.html (953 words)

	[No title]
		If we had a boundary condition expressed as a gradient or mixed boundary condition, the boundary temperature would not be known, but we would have an additional finite-difference equation to solve for the unknown boundary temperature.
		At the boundaries, where the temperatures are known, the error is zero.
		In this example, we know that the boundary temperature is given as T0 = TA from the boundary condition from the original problem in equation [2-33].
	www.csun.edu /~lcaretto/me501a/introNumCalc.doc (4499 words)

	FlexPDE User's Forum: How to implement iteration algorithm in FlexPDE?
		At the beginning of the iterative algorithm, part of the boundary conditions is unknown and zero value is used as initial guessing to solve the PDE(Laplace equation).
		In each iteration, the boundary condition will be updated according to the solution of previous iteration.Finally the accurate solution can be obtained.
		In my algorithm, the type of the boundary condition for a boundary is changing from one stage to next stage.
	www.pdesolutions.com /cgi-bin/discus/show.cgi?tpc=4&post=926 (540 words)

	[No title]
		The distinction here is that the boundary condition (6.2) is homogeneous and the characteristic wavenumbers k
		For the Helmholtz eigenvalue problem with the general boundary condition (6.2) the integral equation formulation is as follows:
		For the more general Robin condition (6.2) the eigenproblem cannot be written so concisely; it is the solution of (6.9) subject to the boundary condition (6.2).
	www.boundary-element-method.com /acoustics/manual/chap6/sect6_1.htm (224 words)

	[No title]
		On the other hand, the left and right edges are at 0 # degrees, so heat flows from the edges to the cold spots, and from the # hot spots to the edges.
		The advantage of taking the first # interpretation is that another solution that satisifies the same # boundary conditions can be added to this one and the sum of the two # solutions will still satisfy the boundary conditions because 0+0=0.
		# # If we impose the boundary conditions which T satisfies, then we can # check if T is a steady state solution of the heat equation with these # boundary conditions.
	www.math.utah.edu /~charris/3150proj1.txt (1575 words)

	Functional Relationship to Describe Drains with Entrance Resistance (Site not responding. Last check: 2007-10-13)
		If soil is saturated, drains act as the Dirichlet boundary condition with pressure head set equal to zero, and if soil is unsaturated, drains act as the Neumann boundary condition with flow set equal to zero.
		To account for the resulting resistance, a Hooghoudt–type boundary condition was developed that prescribes drain flow in relation to the groundwater level at a reference position.
		With a correctly formulated and calibrated Hooghoudt boundary condition, however, more accurate drain discharges were obtained.
	www.pubs.asce.org /WWWdisplay.cgi?0106814 (208 words)

	Boundary conditons for the k-equation (k-epsilon style)
		Computes prescribed and flux boundary conditions for the transport equation (150).
		The Dirichlet (prescribed) boundary condition follows from (101) as
		The Dirichlet (prescribed) boundary condition follows simply from the power-law in (108),
	www.gotm.net /pages/documentation/manual/html/node59.html (176 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		It turns out that the location of the peaks is determined by the non-autonomous term of the equation and the type of the boundary condition.
		Our results are based on fine estimates of the energies of the solutions and some non-existence results for semilinear equations on half spaces with Dirichlet boundary condition and some decay conditions at infinity.
		In this paper we shall show that the least-energy solutions of (1.1) with either the Dirichlet boundary condition or the Neumann boundary condition develop spiky pattern of single peak as $\epsilon$ approaches $0$.
	www.maths.tcd.ie /EMIS/journals/EJDE/Monographs/Volumes/Volumes/1993/05-Ren/Ren-tex (3765 words)

	Elliptic control problems with Dirichlet boundary conditions
		Instead of trying to prove first order necessary conditions under strong assumptions we content ourselves with deriving first order necessary conditions in a purely formal way.
		This form of the necessary conditions will be justified by its analogy in the first order necessary conditions for the discretized version of the elliptic problem; cf.
		be multipliers associated with the elliptic equation and the Dirichlet boundary condition in (3.2), and let
	plato.la.asu.edu /papers/paper84/node3.html (321 words)

	The Home Page of R. Bruce Kellogg (Site not responding. Last check: 2007-10-13)
		This paper studies the boundary layers and corner singularities of a self-adjoint problem in a plane polygonal domain.
		This paper, by Kellogg and Stynes, studies the interior layer that results from a jump discontinuity in the Dirichlet boundary condition.
		II.2.2 The equation in a sector - Dirichlet conditions (5pp)
	www.math.sc.edu /~kellogg (536 words)

	Inverse Obstacle Scattering
		In addition to the above, there is a boundary condition on the scatter itself.
		A further issue of considerable practical interest is to determine the type of boundary of the unknown obstacle for this cannot always be assumed as known.
		In a slightly different direction, we have completed a paper [KR3] that showed unique recovery of a scattering obstacle with boundary B from measurement of the far field at isolated points.
	www.math.tamu.edu /~william.rundell/obstaclescat.html (932 words)

	6.5.2 Separating the streamfunction's boundary value problem (Site not responding. Last check: 2007-10-13)
		The purpose of this section is to develop an algorithm for solving the streamfunction's boundary value problem (BVP).
		The first one is a forced elliptical problem with homogeneous boundary conditions
		The second BVP is a time-independent unforced elliptical problem with constant boundary conditions on the islands
	www.ocgy.ubc.ca /~yzq/books/MOM3/s2node56.html (145 words)

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