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+# Heat equation solver with a pseudo-spectral method
+
+(SP4E 2018, Homework 3)
+Authors: Sajjad Azimi, Alessia Ferraro
+
+
+## Description
+The main.cc program is written to construct and solve a physical problems related to system of particles. In this specific
+case the goal is to solve the 2-dim heat equation with a given source term constant in time. To do so a basic pseudo-spectral
+method is implemented, making use of finite differences in time and spectral discretization in space with Fourier expansion
+in x and y directions.
+
+The relevant classes for the implementation are the following:
+
+* **MaterialPoint**: Class derived from Particles, containing spatially located virtual massless particles that carry a
+temperature and an heat-transfer value.
+
+* **MaterialPointFactory**: Class responsible for the creation of the specific simulation that solves the heat transfer equation.
+It derives from the ParticleFactory interface and builds the system with the suitable type of particles and solver.
+
+* **Matrix**: Storage Class for the temperature and the heat-transfer values of each particles in the domain. Each element (i,j)
+represents a position in the physical space with the corresponding values of these scalar quantities.
+
+* **FFT**: Wrapping interface for FFTW. Class responsible to compute forward and backward DFT for input matrices.
+
+
+
+
+
+
+### Workflow (ex 2.1)
+
+Because of the modular structure of the project, the work was naturally divided between the two authors as follows:
+* Alessia Ferraro: Implementation of the ComputeTemperature class and related functions in the Matrix class (exercises 4)
+* Sajjad Azimi: Implementation of the FFT interface (exercises 3)
+
+The main program, as well as the small adjustments to the common methods, were implemented together in order to achieve
+a uniform structure.
+
+
+