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Sandu split Allen-Cahn #142

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66cb5bb
Allen Cahn splitting added
adrian-sandu Sep 1, 2026
4b3de2c
AS on AllenCahn
adrian-sandu Sep 1, 2026
ff2533c
Linear-nonlinear splitting of Allen-Cahn
adrian-sandu Sep 1, 2026
7f5567e
Split Allen-Cahn into diffusion and reaction parts
adrian-sandu Sep 1, 2026
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9 changes: 9 additions & 0 deletions toolbox/+otp/+allencahn/f_diffusion.m
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% Process splitting:

@AndreyAPopov AndreyAPopov Sep 1, 2026

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Steven: We need to add these functions to the problem file.

@Steven-Roberts Steven-Roberts Sep 2, 2026

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Yes, here is an example

ODE-Test-Problems/toolbox/+otp/+brusselator/BrusselatorProblem.m

Lines 88 to 94 in 167bdc1

obj.RHSLinear = otp.RHS(@(t, y) otp.brusselator.fLinear(t, y, a, b), ...
'Jacobian', otp.brusselator.jacobianLinear(a, b), ...
'Vectorized', 'on');
obj.RHSNonlinear = otp.RHS(@(t, y) otp.brusselator.fNonlinear(t, y, a, b), ...
'Jacobian', @(t, y) otp.brusselator.jacobianNonlinear(t, y, a, b), ...
'Vectorized', 'on');

% f = f_diffusion + f_reaction
% Jacobian = Jacobian_diffusion + Jacobian_reaction
%
function du = f_diffusion(~, u, L, alpha, ~, ~)

@AndreyAPopov AndreyAPopov Sep 1, 2026

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please rename to fDiffusion, we do not use underscores in OTP


du = alpha*L*u;

end
8 changes: 8 additions & 0 deletions toolbox/+otp/+allencahn/f_linear.m
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% Linear-nonlinear splitting: f = f_linear + f_nonlinear
% f_linear(u) = Jac*u, f_nonlinear(u) = f(u)-Jac*u

function du = f_linear(~, u, L, alpha, beta, ~)

@AndreyAPopov AndreyAPopov Sep 1, 2026

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fLinear


du = alpha*L*u + beta * (u - 3*u.^3);

@Steven-Roberts Steven-Roberts Sep 2, 2026

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Is this correct? It looks like it has nonlinear terms.

@reid-g reid-g Sep 2, 2026

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The goal is to create the splitting $y' = J(y) y + (f(y) - J(y) y)$ where the linear split term is $y' = J(y) y$. So this is correct given the nonlinear term $f(u) = u - u^3$.
However, we may want separate evaluation of $ J(z) y$ ( e.g. $J(y_{n}) y$) but, I think that maybe out of scope here for now.

@Steven-Roberts Steven-Roberts Sep 3, 2026

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I see. In that case, I think the names are ok as long as it is documented. Alternatively, you could consider calling them RHSJacobian and RHSRemainder.


end
8 changes: 8 additions & 0 deletions toolbox/+otp/+allencahn/f_nonlinear.m
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% Linear-nonlinear splitting: f = f_linear + f_nonlinear
% f_linear(u) = Jac*u, f_nonlinear(u) = f(u)-Jac*u

function du = f_nonlinear(t, u, ~, ~, beta, forcing)

@AndreyAPopov AndreyAPopov Sep 1, 2026

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fNonlinear


du = beta * (u - u.^3) - beta * (u - 3*u.^3) + forcing(t);

end
9 changes: 9 additions & 0 deletions toolbox/+otp/+allencahn/f_reaction.m
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% Process splitting:
% f = f_diffusion + f_reaction
% Jacobian = Jacobian_diffusion + Jacobian_reaction
%
function du = f_reaction(t, u, ~, ~, beta, forcing)

@AndreyAPopov AndreyAPopov Sep 1, 2026

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fReaction


du = beta * (u - u.^3) + forcing(t);

end
9 changes: 9 additions & 0 deletions toolbox/+otp/+allencahn/jacobian_diffusion.m
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% Process splitting:
% f = f_diffusion + f_reaction
% Jacobian = Jacobian_diffusion + Jacobian_reaction
%
function j = jacobian_diffusion(~, ~, L, alpha, ~, ~)

@AndreyAPopov AndreyAPopov Sep 1, 2026

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jacobianDiffusion


j = alpha*L;

end
9 changes: 9 additions & 0 deletions toolbox/+otp/+allencahn/jacobian_reaction.m
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% Process splitting:
% f = f_diffusion + f_reaction
% Jacobian = Jacobian_diffusion + Jacobian_reaction
%
function j = jacobian_reaction(~, u, L, ~, beta, ~)

@AndreyAPopov AndreyAPopov Sep 1, 2026

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jacobianReaction


j = spdiags(beta * (1 - 3*u.^2), 0, size(L, 1), size(L, 2));

end
58 changes: 56 additions & 2 deletions toolboxPackaging.prj
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@@ -1,5 +1,5 @@
<deployment-project plugin="plugin.toolbox" plugin-version="1.0">
<configuration name="ODE Test Problems" target="target.toolbox" target-name="Package Toolbox">

@AndreyAPopov AndreyAPopov Sep 1, 2026

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please don't commit this file, so please git revert this file

<configuration file="/Users/sandu/GIT/GitHub/ODE-Test-Problems/toolboxPackaging.prj" location="/Users/sandu/GIT/GitHub/ODE-Test-Problems" name="toolboxPackaging" target="target.toolbox" target-name="Package Toolbox">
<param.appname>ODE Test Problems</param.appname>
<param.authnamewatermark>Steven Roberts, Andrey A. Popov, Arash Sarshar, Adrian Sandu</param.authnamewatermark>
<param.email />
Expand All @@ -14,7 +14,7 @@
<param.products.version />
<param.platforms />
<param.guid>0970ed36-a788-484f-beca-105eecd2562a</param.guid>
<param.exclude.filters></param.exclude.filters>
<param.exclude.filters />
<param.exclude.pcodedmfiles>true</param.exclude.pcodedmfiles>
<param.examples />
<param.demosxml />
Expand Down Expand Up @@ -85,5 +85,59 @@
<fileset.depfun.included />
<fileset.depfun.excluded />
<fileset.package />
<build-deliverables>
<file location="${PROJECT_ROOT}" name="ODE Test Problems.mltbx" optional="false">/Users/sandu/GIT/GitHub/ODE-Test-Problems/ODE Test Problems.mltbx</file>
</build-deliverables>
<workflow />
<matlab>
<root>/Applications/MATLAB_R2024b.app</root>
<toolboxes>
<toolbox name="matlabcoder" />
<toolbox name="embeddedcoder" />
<toolbox name="fixedpoint" />
<toolbox name="matlabhdlcoder" />
<toolbox name="neuralnetwork" />
</toolboxes>
<toolbox>
<matlabcoder>
<enabled>true</enabled>
</matlabcoder>
</toolbox>
<toolbox>
<embeddedcoder>
<enabled>true</enabled>
</embeddedcoder>
</toolbox>
<toolbox>
<fixedpoint>
<enabled>true</enabled>
</fixedpoint>
</toolbox>
<toolbox>
<matlabhdlcoder>
<enabled>true</enabled>
</matlabhdlcoder>
</toolbox>
<toolbox>
<neuralnetwork>
<enabled>true</enabled>
</neuralnetwork>
</toolbox>
</matlab>
<platform>
<unix>true</unix>
<mac>true</mac>
<windows>false</windows>
<win2k>false</win2k>
<winxp>false</winxp>
<vista>false</vista>
<linux>false</linux>
<solaris>false</solaris>
<osver>15.5</osver>
<os32>true</os32>
<os64>false</os64>
<arch>maci64</arch>
<matlab>true</matlab>
</platform>
</configuration>
</deployment-project>
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