In this tutorial, we will explore how to create and excite a Gaussian pulse in COMSOL Multiphysics—an essential technique used across multiple physics domains including acoustics, electromagnetics, structural dynamics, and heat transfer. The Gaussian pulse is known for its smooth, localized shape, which makes it ideal for studying system responses without introducing artificial high-frequency content or numerical noise. Whether you're modeling ultrasonic wave propagation, laser heating, or transient pressure waves, this step-by-step guide will help you understand the practical setup, implementation, and application of Gaussian pulses in COMSOL.
A Gaussian pulse is defined mathematically as:
$$
\text{Pulse}(t) = \exp\left(-\frac{(t - t_0)^2}{2\sigma^2} \right)
$$
This expression represents a time-localized signal centered at $t_0$ with a width controlled by the standard deviation $\sigma$. In this tutorial, we use the following values for practical implementation:
- $t_0 = 5 \times 10^{-5}$ seconds (50 microseconds)
- $\sigma = 5 \times 10^{-6}$ seconds (5 microseconds)
Substituting these into the expression gives us:
$$
\text{Pulse}(t) = \exp\left(-\frac{(t - 5 \times 10^{-5})^2}{2 \cdot (5 \times 10^{-6})^2} \right)
$$
To implement this in COMSOL Multiphysics, navigate to Definitions > Functions > Analytic, and define a new function with the above expression. This pulse can be applied as a time-dependent source term in a variety of physics interfaces such as pressure in acoustics, force in solid mechanics, or heat flux in thermal simulations.
Let’s explore real-world applications where this Gaussian pulse is practically used:
| Application Domain | Description |
|---|---|
| Acoustics | Simulates a clean sound burst for analyzing echo patterns, refraction, and material defects (NDT). |
| Structural Mechanics | Used as a transient load to study vibration, damping, and resonance in mechanical structures. |
| Thermal Analysis | Models sudden heating events, such as laser pulses or thermal spikes, to evaluate heat diffusion. |
| Electromagnetic Waves | Ideal for simulating transient EM propagation and antenna excitation without continuous waveforms. |
| Impulse Response Analysis | Applied across domains to examine system behavior in response to short, sharp inputs. |
In addition, we can define a damped sinusoidal pulse for scenarios where an oscillatory input is needed:
$$
\text{Pulse}(t) = \exp\left(-\frac{(t - 5 \times 10^{-5})^2}{2 \cdot (5 \times 10^{-6})^2} \right) \cdot \sin(2\pi \cdot 10^6 \cdot t)
$$
This represents a Gaussian-modulated sine wave—a useful input for more realistic scenarios involving wave propagation in lossy media.
By the end of the video, you will know how to:
- Define a Gaussian pulse using an analytic function
- Assign it to a boundary or domain source in COMSOL
- Customize its width and center timing
- Apply it in multiphysics studies like pressure acoustics, solid mechanics, and transient thermal simulations
This tutorial is perfect for students, researchers, and engineers working in simulation-driven environments. It also provides foundational knowledge applicable in RF, NDT, optics, and other advanced simulation fields.
To watch the full walkthrough and see the simulation results, check out the full video on Learn with BK.
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