PERIDYNAMICS_1D_STEADY
Steady 1D Poisson Equation
Nonlocal Peridynamics Model
PERIDYNAMICS_1D_STEADY
a MATLAB library which
solves a 1D steady version of the Poisson equation,
using the nonlocal peridynamics model,
by Marta D'Elia.
The problem data is specified by a usersupplied file which evaluates:

the exact solution u(x);

the derivative of the exact solution u'(x).

the right hand side of the Poisson equation, u"(x).

the lifting, a function which adjusts the problem for nonzero Dirichlet
boundary conditions;
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
PERIDYNAMICS_1D_STEADY is available in
a MATLAB version.
Related Data and Programs:
PERI1D,
a C program which
sets up and solves a 1D timedependent peridynamics problem,
by Miroslav Stoyanov;
Author:
Marta D'Elia
Reference:

Qiang Du, Max Gunzburger, Rich Lehoucq, Kun Zhou,
Analysis and approximation of nonlocal diffusion problems
with volume constraints,
SIAM Review,
Volume 54, Number 4, pages 667696, 2012.

Max Gunzburger, Rich Lehoucq,
A nonlocal vector calculus with application to nonlocal boundary
value problems,
Multiscale Modeling and Simulation,
Volume 8, Number 5, 2010, pages 15811598.
Source Code:
Examples and Tests:

pd1d_steady_test.m,
calls both convergence tests for all problems. You probably
don't want to call this function, but it shows you how to call
either test below for any of the five sample problems.

pd1d_steady_test01.m,
for a given problem (1, 2, 3, 4 or 5), this test computes convergence results
as EPSILON and H go to zero in fixed ratio.
You specify the problem as an input quantity that is a MATLAB function handle,
such as "@problem1".

pd1d_steady_test02.m,
for a given problem (1, 2, 3, 4 or 5), this test computes convergence results
for fixed EPSILON, while H goes to zero.
You specify the problem as an input quantity that is a MATLAB function handle,
such as "@problem5".
PROBLEM 1 has the solution U(X) = X^2, on the domain [0,1].
PROBLEM 2 has the solution U(X) = X^2*(1X^2), on the domain [0,1].
PROBLEM 3 has the solution U(X) = X^2, on the domain [0,1].
PROBLEM 4 has the solution U(X)=X1/4 left of 1/2, and U(X)=X1/2
to the right of 1/2, on the domain [0,1]. This problem was devised to
study the behavior of singularities.
PROBLEM 5 has the solution U(X) = 1+X, on the domain [0,1].
This problem was devised for a simple accuracy check.
You can go up one level to
the MATLAB source codes.
Last modified on 29 February 2012.