Maximum intensity for planar source

[zhang haohui]

Hello, Prof. Fang,

In the following code, I applied a planar source 20*20 and try to find the maximum intensity in the body. The maximum intensity is under the source and equal to 8.5e-3. However, according to my understanding, when 1 unit power is applied, the maximum intensity should be 1/(20^2) = 2.5e-3. Why the computed maximum intensity is much larger than this value?

I also tried different area and the point source. It is always the case. 

Thank you very much!

Best wishes 

Haohui

clear cfg

cfg.nphoton=1e8;

cfg.outputtype='fluence';

cfg.seed = 77542;

cfg.vol=ones(200,200,200);

cfg.prop = [0,0,0,1;0.006,1.3,0,1];

% light source

cfg.srctype = 'planar';

cfg.srcpos=[0,90.5,90.5];

cfg.srcparam1=[0,20,0];

cfg.srcparam2=[0,0,20];

cfg.srcdir=[1,0,0];

cfg.issrcfrom0=1;

% time windows

cfg.tstart=0;

cfg.tend=1e-8;

cfg.tstep=1e-9;

% other simulation parameters

cfg.isspecular=1;

cfg.isreflect=1;

cfg.autopilot=1;

cfg.gpuid=1;

cfg.issaveref=1; % save diffuse reflectance

% Unit length

% cfg.unitinmm = 0.6;

% Detector

cfg.detpos=[20,20,20,2];

tic

%% run MCX simulation

flux = mcxlab(cfg);

toc

%% post-simulation data processing and visualization

% convert time-resolved fluence to CW fluence

CWfluence=sum(flux.data,4);

cwdref=sum(flux.dref,4); % diffuse reflectance

max(CWfluence,[],'all')

[Qianqian Fang]

hi Haohui

this is a misunderstanding of a unitary source.

if you look at the Green's function of fluence for the diffusion equation in the infinite space

Phi = 1/(4*pi*D).*[exp(-k*r)./r ]

where r is the distance to the source, you can see that Phi(r=0) is infinity - so if you are looking for the maximum value of the fluence, it is infinity in continuous space.

On 12/11/23 00:57, zhang haohui wrote:

Hello, Prof. Fang,

In the following code, I applied a planar source 20*20 and try to find the maximum intensity in the body. The maximum intensity is under the source and equal to 8.5e-3. However, according to my understanding, when 1 unit power is applied, the maximum intensity should be 1/(20^2) = 2.5e-3. Why the computed maximum intensity is much larger than this value?

if you are looking for something that can sum up to 1, you are looking for energy deposition. in this case, you should set cfg.output to 'energy'.

the sum of the energy deposition should be equal to the absorption fraction printed at the bottom of mcx's simulation log.

Qianqian

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[zhang haohui]

Hello, Prof. Fang,

Regarding the matter at hand, I believe the issue isn't directly related to the diffusion equation, given that we're utilizing Monte Carlo methods to tackle the problem. Specifically, at r=0, the apparent infinity intensity stems from the point source—a characteristic inherent to point sources resulting in an infinite intensity.

However, the discrepancy arises from my use of a planar source, which eliminates the concept of an infinite source. Despite this, I've observed a maximum intensity of 8.5e-3 uniformly across first layer of the bulk material under the irradiated area, exceeding the source intensity, which appears to be inaccurate.

I have verified the total energy deposition within the codes is correct. Please let me know if there's any ambiguity in my explanation or if further details are required. Your insights into this matter are greatly appreciated.

Best wishes

Haohui

[Qianqian Fang]

again, you can not directly translate the norm of the source-term (right-hand-side/RHS) to the max/norm of the solution of a PDE/or integral-differential equation like RTE

in many cases, a PDE/integral-differential equation can be represented by a linear operator, L(), and the PDE can be solved as

L(Phi)=S

where S is the source; this gives you Phi = inv(L)(S)

if L is a linear matrix, like in FEM/finite-difference, i.e. L=A where A is a matrix, then Phi=inv(A)*S

the max/norm of solution Phi depends on the eigenvalues of the system matrix A, and they not 1 in most cases.

To view this discussion on the web visit https://groups.google.com/d/msgid/mcx-users/aa2b0f99-1457-49d5-ba5a-821bbce52c0fn%40googlegroups.com.

[zhang haohui]

Hello, Prof. Fang,

Thanks for your very helpful understanding. I will think over it.

Best wishes

Haohui