rbfpeval.m

本代码为基于matlab的求解偏微分方程的利用径向基函数的无网格方法的源码

function values = rbfPeval (evalpoints, intpoints, bndpoints, coeff)  
% evaluate at evalpoints
% an RBF approximation to a Poisson problem defined by centers in intpoints and bndpoints,
% using coeff as a general vector of coefficients
global RBForder;
[numeval,evaldim]=size(evalpoints);
[numint,intdim]=size(intpoints);
[numbnd,bnddim]=size(bndpoints);
[numcoeff,coeffdim]=size(coeff);
if evaldim~=intdim
    error('Unequal dimensions for evaluation and interior points')
end
if evaldim~=bnddim
    error('Unequal dimensions for evaluation and boundary points')
end
if numcoeff~=numint+numbnd+RBForder+(RBForder*(RBForder-1)*(evaldim-1))/2
    error('Number of data points must match number of coefficients')
end
if coeffdim~=1
    error('Coefficients must be a vector')
end
evalsquares=sum(evalpoints.^2,2);
intsquares=sum(intpoints.^2,2);
bndsquares=sum(bndpoints.^2,2);
if RBForder==0
    fullmat=[rbfLaplace(sqrt(repmat(evalsquares,1,numint)+repmat(intsquares,1,numeval)'...
        -2*evalpoints*intpoints'))...
        rbf(sqrt(repmat(evalsquares,1,numbnd)+repmat(bndsquares,1,numeval)'...
        -2*evalpoints*bndpoints'))];
elseif RBForder==1  
        fullmat=[rbfLaplace(sqrt(repmat(evalsquares,1,numint)+repmat(intsquares,1,numeval)'...
        -2*evalpoints*intpoints'))...
        rbf(sqrt(repmat(evalsquares,1,numbnd)+repmat(bndsquares,1,numeval)'...
        -2*evalpoints*bndpoints'))...
        ones(numeval,1)];
elseif RBForder==2
        fullmat=[rbfLaplace(sqrt(repmat(evalsquares,1,numint)+repmat(intsquares,1,numeval)'...
        -2*evalpoints*intpoints'))...
        rbf(sqrt(repmat(evalsquares,1,numbnd)+repmat(bndsquares,1,numeval)'...
        -2*evalpoints*bndpoints'))...
        ones(numeval,1) evalpoints];
end
values=fullmat*coeff;