chunkie
chunkie is a MATLAB package for solving partial differential equations in two dimensional domains. The name “chunkie” derives from the use of chunks (panels with scaled Legendre nodes) to discretize the domain boundary and the use of an integral equation method to solve the PDE.
With chunkie, you can solve the Helmholtz equation on an exterior domain in a few lines of MATLAB. The code below defines and solves a scattering problem, producing the image above:
% planewave definitions
kvec = 20*[1;-1.5];
zk = norm(kvec);
planewave = @(kvec,r) exp(1i*sum(bsxfun(@times,kvec(:),r(:,:)))).';
% discretize domain
chnkr = chunkerfunc(@(t) starfish(t,narms,amp),struct('maxchunklen',4/zk));
% build CFIE and solve
fkern = kernel('helm','c',zk,[1,-zk*1i]);
sysmat = chunkermat(chnkr,fkern);
sysmat = 0.5*eye(chnkr.k*chnkr.nch) + sysmat;
rhs = -planewave(kvec(:),chnkr.r(:,:));
sol = gmres(sysmat,rhs,[],1e-13,100);
% evaluate at targets
x1 = linspace(-3,3,400);
[xxtarg,yytarg] = meshgrid(x1,x1);
targets = [xxtarg(:).';yytarg(:).'];
in = chunkerinterior(chnkr,targets);
out = ~in;
uscat = chunkerkerneval(chnkr,fkern,sol,targets(:,out));
uin = planewave(kvec,targets(:,out));
utot = uscat(:)+planewave(kvec,targets(:,out));
% plot
maxu = max(abs(utot(:)));
figure()
zztarg = nan(size(xxtarg));
zztarg(out) = utot;
h=pcolor(xxtarg,yytarg,imag(zztarg));
set(h,'EdgeColor','none')
hold on
plot(chnkr,'LineWidth',2)
axis equal tight
colormap(redblue)
caxis([-maxu,maxu])
Features
easy-to-use: most chunkie functionality only requires that you specify two things, the geometry (as a “chunker” object) and the integral kernel (as a “kernel” object). The distribution includes pre-defined kernels for the Laplace, Helmholtz, and Stokes PDEs and convenient tools for visualizing domains and plotting solutions.
capable: chunkie uses high order accurate quadrature rules and fast algorithms to provide accurate solutions with linear scaling. The chunkie utilities can be used to solve singular problems on domains with corners and multiple material junctions with relative ease.
flexible: allows you to define your own integral kernels and use the quadrature routines in a modular fashion.
How to Get Chunkie
Get chunkie (includes installation instructions and troubleshooting guide)
Using Chunkie
The chunkie guide provides an overview of the chunkie approach to PDEs and a detailed look at chunkie’s capabilities.
Gallery
The gallery has examples of chunkie applications submitted by users.
Contributing
We welcome your collaboration! First, see the developer guide.
License
The project is licensed under a modified BSD 3-clause license.
Contents