Re: How can we speed up the rate of photosynthesis,??????

You are correct that increasing the light level is one way to increase 
photosynthesis for most plants, assuming they aren't shade plants where 
increasing light too much will actually reduce photosynthesis. The light can be 
increased with electric lights, either by raising the light level or by 
providing light longer each day. Light level might be increased by changing 
locations, by cutting down surrounding plants that are shading your plant and 
by increasing the spacing between plants. You can also do something exotic like 
use mirrors to increase the light level.

The general equation for photosynthesis provides two more possible ways to 
increase photosynthesis, i.e. by raising the concentration of the reactants. 

Other common limitations to plant growth, and thus photosynthesis, are:
1.  deficiency of mineral nutrients, especially nitrogen
2.  toxicity of mineral nutrients, such as boron or zinc
3.  toxicity of other elements, such as sodium or chromium
4.  soil pH too high or too low 
5.  high soil salinity
6.  diseases
7.  insects and other pests 
8.  temperatures too high or too low
9.  soil provides too much mechanical resistance to root growth
10. for C-3 plants under high light and high temperatures, the normal level of 
oxygen in the atmosphere causes photorespiration, which reduces photosynthesis
11. competition from other plants, including allelopathy
12. air pollution, such as acid rain

Two general ways to optimize plant growth or photosynthesis are to grow plants 
in greenhouses or growth chambers where the environment can be more easily 
optimized. Another approach to increasing plant growth or photosynthesis is 
breeding and selection of faster growing or higher yielding plants.

Reference


What happens during the process called "photorespiration"?


Photosynthesis limitation