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Non Hermitian Acoustic Model

Posted 2025年8月2日 GMT+8 08:09 Version 6.0 0 Replies

Md. Anzan-Uz-Zaman

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I'm summarizing my whole work.

With COMSOL 6.2. Non-Hermitian Study with Balanced Loss and gain with only COMSOL Weak Form PDE. I have an Hamiltonian, H=[0 (v+gamma)+w.exp(-ik);(v-gamma)+w.exp(-ik) 0]. I tried weak form of equation.

Model Details: 1. Parameter: L=60[mm], kx=pi/L, h1=5[mm], r=5[mm] g=1[1/m], c_air=343[m/s], rho_air=1[kg/m^3], k=1 [1/m].

Geometry: Rectangle1 (Width L/2, Height h1, Position, x=0, y=0); Rectangle2 (Width L/2, Height h1, Position, x=L/2, y=0); Circle1(Radius r, Position, x=L/4 y=h1/2), Circle2(Radius r, Position, x=3L/4 y=h1/2). Then Union. Then delete Entities to delete internal boundaries inside the circle.
Materials: Now we have 5 domains. Domain 2 is the channel between between circles A (domain 4) and B (domain 5). We used user defined materials. Material Type: Non-Solid, Speed of sound, c=c_air and density, rho=rho_air. All the domains have same material properties.
In Component 1> Definitions>Identity Boundary Pair 1, I selected Source boundary as Left (1) boundary and Destination boundary as Right (10) Boundary.
Weak form of PDE: Applied to Domain all Domain. Weak Form PDE 1< Weak Expressions: - (test(px)px + test(py)py)+ ((2pifreq/c_air)^2)test(p)p.

Then took Weak Form PDE 2 and selected only Domain 2 and put expression: igtest(p)*px. This is non-reciprocity term.

Next, for Periodic Condition, I used Weak Form PDE (w) >Pair> Weak Contribution. Then at Pairs section selected the predefined "Identity Boundary Pair 1". And at Weak expression field, wrote expression as "test(p)(p - dest(p)exp(ikxL))".

Mesh: Free Triangular with Predefined size 'fine'.
Study 1: Parametric Sweep: g=0:0.01:1 and kx=0:0.1*pi/L:pi/L. Step1: Eigenvalue, Desired number of eigenvalues 6 and Search for eigenfrequencies around 1+1i[rad/s].

I run the simulation. There was no error. But, the periodic condition "test(p)(p - dest(p)exp(ikxL))" is not working. How to solve ?

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