Add to ORKGThroughout many fields of science and engineering, the need for describing waveequations is crucial. Solving the wave equation for high-frequency waves istime-consuming, requires a fine mesh size and memory usage. The main goal wasimplementing and comparing different solution methods for high-frequency waves.Four different methods have been implemented and compared in terms of runtimeand discretization error. From my results, the method which performs the best is thefast sweeping method. For the fast marching method, the time-complexity of thenumerical solver was higher than expected which indicates an error in myimplementation.
We build Gaussian wave packets for the linear Schrödinger equation and its finite difference space s...
This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/87...
A wide variety of problems can be formulated as an interface propagation. Some examples are burning ...
Throughout many fields of science and engineering, the need for describing waveequations is crucial....
textHigh-frequency wave phenomena is observed in many physical settings, most notably in acoustics, ...
The problem of simulating the scattering of (acoustic, electromagnetic, elastic) waves has provided ...
The main focus of this thesis is on fast numerical methods, where adaptivity is an important mechani...
We consider observables (quantities of interest) of the wave equation where the initial data has a w...
This paper presents a numerical method for “time upscaling ” wave equations, i.e., performing time s...
Abstract. This paper presents a numerical method for “time upscaling ” wave equations, i.e., perform...
Waves of diverse types surround us. Sound, light and other waves, such as microwaves, are crucial fo...
It is often noted that the Helmholtz equation is extremely difficult to solve, in particular, for hi...
High frequency wave propagation problems are computationally costly to solve by traditional techniqu...
AbstractIt is often noted that the Helmholtz equation is extremely difficult to solve, in particular...
Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves ...
We build Gaussian wave packets for the linear Schrödinger equation and its finite difference space s...
This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/87...
A wide variety of problems can be formulated as an interface propagation. Some examples are burning ...
Throughout many fields of science and engineering, the need for describing waveequations is crucial....
textHigh-frequency wave phenomena is observed in many physical settings, most notably in acoustics, ...
The problem of simulating the scattering of (acoustic, electromagnetic, elastic) waves has provided ...
The main focus of this thesis is on fast numerical methods, where adaptivity is an important mechani...
We consider observables (quantities of interest) of the wave equation where the initial data has a w...
This paper presents a numerical method for “time upscaling ” wave equations, i.e., performing time s...
Abstract. This paper presents a numerical method for “time upscaling ” wave equations, i.e., perform...
Waves of diverse types surround us. Sound, light and other waves, such as microwaves, are crucial fo...
It is often noted that the Helmholtz equation is extremely difficult to solve, in particular, for hi...
High frequency wave propagation problems are computationally costly to solve by traditional techniqu...
AbstractIt is often noted that the Helmholtz equation is extremely difficult to solve, in particular...
Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves ...
We build Gaussian wave packets for the linear Schrödinger equation and its finite difference space s...
This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/87...
A wide variety of problems can be formulated as an interface propagation. Some examples are burning ...
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